Global Population, Carrying Capacity, and High-Quality, High-Pressure Processed Foods in the Industrial Revolution Era

Abstract

The report examines food availability and demand in the Anthropocene era, exploring the connections between global population growth and carrying capacity through an extended version of Cohen’s Condorcet concept. It recalls the super-Malthus and Verhulst-type scalings, matched with the recently introduced analytic relative growth rate. It focuses particularly on the ongoing Fifth Industrial Revolution (IR) and its interaction with the concept of a sustainable civilization. In this context, the significance of innovative food preservation technologies that can yield high-quality foods with health-promoting features, while simultaneously increasing food quantities and reducing adverse environmental impacts, is discussed. To achieve this, high-pressure preservation and processing (HPP) can play a dominant role. High-pressure ‘cold pasteurization’, related to room-temperature processing, has already achieved a global scale. Its superior features are notable and are fairly correlated with social expectations of a sustainable society and the technological tasks of the Fifth Industrial Revolution. The discussion is based on the authors’ experiences in HPP-related research and applications. The next breakthrough could be HPP-related sterilization. The innovative HPP path, supported by the colossal barocaloric effect, is presented. The mass implementation of pressure-related sterilization could lead to milestone societal, pro-health, environmental, and economic benefits.

1. Introduction

The last Ice Age, which lasted around 100,000 years, ended 12,000 years ago. Global warming then freed vast areas of Eurasia and North America from ice sheets. The mild climate, vast uninhabited areas, and rich food resources yielded exceptional opportunities for hunter–gatherers. This marked the beginning of the Anthropocene era [1]. Over only 12 millennia, the global population rose from $~2\mathrm{m}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{o}\mathrm{n}$ in 10,000 BCE to $~8.23\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{o}\mathrm{n}$ in June 2025 [2,3,4]. This population growth was largely due to millennia of access to seemingly ‘infinite’ food resources for an ever-increasing population. Food is a vital source of energy, essential for maintaining good health. Ensuring that any person and any family has enough food is a daily challenge. Consequently, the question of the impact of this essential resource on the global population changes since the onset of the Anthropocene arises.

This report aims to provide a preliminary response.

The answer may seem puzzling due to the vast and multidimensional scope of changes involved, as well as the heterogeneity of the relevant issues. However, such data may be hidden within the global population growth scaling pattern, which is significantly shaped by access to food resources. For millennia, the exponential growth of the global population was the dominant trend. This is also known as geometric growth, where the growth rate is proportional either to the current population size or to the same relative percentage in each subsequent period [2,3,4]. Recently, explicit evidence of this pattern was also found for a particularly significant period in modern history: from the Middle Ages to the beginning of the Enlightenment era. A qualitatively new ‘boosted’ scaling of global population growth emerged later, spanning $~1700$ to the present [2,3,4]:

$$\begin{array}{l}P\left(t\right)=P_{0}exp\left(rt\right)=P_{0}exp\left({\displaystyle \frac{t}{\tau }}\right)\Rightarrow P\left(t\right)=P_{0}exp\left({\displaystyle \frac{b^{\prime }t}{T_C-t}}\right)=P_{0}exp\left(b{T}^{-1}\right)\\ ~1100-1720\left(‘Malthus’\right)\Rightarrow ~1720-2024(‘\mathit{constrained}\mathit{criticality}’),\end{array}$$

(1)

where $P\left(t\right)$ denotes the global population; $t$ is the time since the onset of the Anthropocene, i.e., 12,000 BCE; $b^{\prime }=const$, $T_C\approx 2216$ is the extrapolated, singular ‘Dooms-year’; $T=\left(T_C-t\right)/t$ is the relative distance from $T_C$; $r=const$ is the Malthus population growth rate parameter; and $\tau =1/r$ is the relaxation time. The latter was introduced for population growth analysis in ref. [2].

Sojecka and Drozd-Rzoska obtained the above result by introducing the super-Malthus (SM) scaling equation, supported by distortion-sensitive analysis [2,3,4]. Notably, this simple exponential behavior, given on the left-hand side of Equation (1), is common in nature, ranging from microbiology and biology to the dynamics of physical processes, chemical reactions, nuclear reactions, and fission reactors. In the latter case, the term ‘chain reaction’ is used to describe the increasing impact of neutrons in subsequent steps [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20].

Over the past two centuries, the global population has grown at an unprecedented rate [21,22], as illustrated on the right-hand side of Equation (1). However, rather than experiencing food shortages, hypermarkets have an apparent surplus of food on their shelves. This extraordinary situation can be explained by technological and societal changes during the Industrial Revolution (IR) era [23,24,25,26]. It is driven by the development and mass implementation of groundbreaking technological innovations, in interplay with socioeconomic ‘innovations’ that support and organize technological development. Progress in the IR era is so rapid that the world can change beyond personal recognition during one person’s lifetime. An example can be seen in the qualitative civilizational changes that occurred during the reigns of two symbolic figures: Emperor Franz Joseph I of Austria (1848–1916) and Queen Victoria I of the United Kingdom (1837–1901) [27,28,29]. Thanks to innovative agricultural technologies, as well as advancements in food processing and logistics, food productivity has increased. This increase in quantity and variety influences the demand. However, this process is only ‘elastic’ to a certain extent. Ultimately, a relative decrease in food prices and lower expenditure are necessary. The funds released to consumers in this way could be spent on other goods and services, thereby stimulating broader economic development. However, these processes could also lead to a decline in agricultural employment. In highly developed countries, only about 10% of all employees work in agriculture nowadays [28,29,30]. A further significant decrease can be expected due to the use of artificial intelligence (AI) in agriculture. The future could involve autonomous agricultural machines that cultivate fields with the support of AI. This concept is depicted in Christopher Nolan’s pioneering film Interstellar (2014).

A key feature of the Industrial Revolution is the ‘feedback mechanism’ between science, technology, and socioeconomic issues. In today’s innovation-driven world, it is essential to develop methods that ensure food safety and extend shelf life while minimizing the impact on the products’ natural state.

The legacy of Louis Pasteur’s work (1863) is of particular importance, as he recognized that the spontaneous development of pathogenic microorganisms posed a significant threat to human health and product safety and quality [31]. He solved this challenge by discovering ‘thermal pasteurization’, i.e., heating a product to $~85°\mathrm{C}$, for a few minutes [32], to achieve a significant reduction in pathogenic microorganisms. In the second half of the 19th century, chemical preservative additives also began to be widely implemented to ensure long-term microbiological safety [33]. During that time, the foundations of refrigeration technology were also developed, making the mass-scale implementation of refrigerators and coolers possible following the first half of the 20th century [34]. Notably, the pioneering works of Pierre Curie and Marie Curie-Skłodowska led to the use of ionic irradiation as a physical factor destructive to microorganisms. The related technology is widely used for dry food products, such as spices [35,36,37].

During the Industrial Revolution period, the development of new food preservation technologies has led to an extraordinary abundance and diversity of foodstuffs on supermarket shelves. Achieving this abundance of food products also required the development of an efficient logistics chain, often on a global scale, which further motivated the search for effective food preservation methods.

However, the dark side of the innovative food preservation methods developed during the IR has been revealed in recent decades. Their accumulation has led to dangerous, harmful, global-scale pandemics related to obesity, allergies, and certain types of cancer [38,39,40,41,42,43,44]. This problem is closely associated with the diverse offer of so-called ultra-processed foods, often chemically modified, containing a set of chemical preservatives and other supplementary artificial additives to make them appealing and addictive. These include numerous carbonated drinks, sweet or salty packaged snacks, ice cream, chocolate, sweets (confectionery), mass-produced bread and rolls, margarines and spreads, cookies (biscuits), energy cakes and bars, energy drinks, milk drinks, ‘fruit’ yogurts and ‘fruit’ drinks, cocoa drinks, meat and chicken extracts, prepared sauces, infant formula, milk substitutes and other products for children, ‘quasi-healthy’ and ‘slimming’ products such as powdered or ‘fortified’ meals and meal substitutes, and many ready-to-eat products, including pre-prepared cakes, pasta dishes and pizza, poultry and fish ‘nuggets’ and ‘sticks’, sausages, burgers, hot dogs and other reconstituted meat products, and powdered and packaged ‘instant’ soups, dumplings, and desserts. It is an offer of products at surprisingly low prices, which may immediately raise suspicions of a connection with so-called ‘junk food’ [45].

Studies have shown that ultra-processed foods increase the risk of obesity by 55%, sleep disorders by 41%, anxiety disorders by 53%, type 2 diabetes by 40%, and depression and premature death by 20%. They also present strong evidence of a 50% increase in the risk of death from cardiovascular disease. It is estimated that approximately 70% of all food in the United States is ultra-processed. Its consumption is responsible for ~6% in Brazil or Chile, and around 14% in the US or England, of the total health problems [45,46]. Therefore, it is not surprising that food waste reaches $>40\%$ globally [47,48].

The simplest and most environmentally friendly way to increase the global food supply is to minimize these losses.

Avoiding the catastrophic impact of ‘junk food’ and the side effects of food preservatives is also essential for the health and well-being of modern societies. The benefits would be incalculable, but, specifically, they would contribute significantly to the world economy.

In the current era of the Fifth Industrial Revolution, ensuring the quantity and variety of food is essential. Providing food that avoids the aforementioned harmful ‘side effects’ has become crucial for modern, ‘sustainable’ societies. This also involves respecting the environment and the circular economy by obtaining more food resources while reducing the disposal of ‘unnecessary’ food and keeping the carbon footprint low.

The basic response to these challenges and civilizational needs is the concept of ‘high-quality foods’, defined as ‘food produced using specific agricultural production methods, in particular in terms of food safety, traceability, authenticity, labelling, nutritional and health values, as well as respect for the environment and animal welfare, the sustainability of agricultural production and distinctive qualities, in particular quality and taste’ [49,50,51].

The fundamental problem lies in the practical implementation of these expectations. This can be achieved by developing new food preservation concepts based on different scientific principles compared to those of the ‘standard’ methods developed in the 19th century, which are still dominant today.

Below, high-pressure preservation and processing (HPP) for foods is presented. This is also termed ‘cold pasteurization’. HPP has already passed market tests and appears to meet all expectations as a next-generation technology for high-quality food processing tools [7,8,52,53,54,55,56,57,58,59,60,61,62,63]. Original solutions for next-generation HPP sterilization are also presented. The preliminary part of the report provides a conceptual background to the above issues, offering a fresh perspective on food needs and requirements in the Anthropocene. The report also discusses the concept of the carrying capacity as a key metric for food and resources. It offers new interpretations of the Condorcet equation, linking population growth and carrying capacity in a functional manner.

2. Materials and Methods

Regarding global population data, this report summarizes the findings of recent studies by various authors on global population growth since the onset of the Anthropocene [2,3,4]. In this case, however, the focus is on the available resources—particularly food—and, more broadly, on the system’s overall carrying capacity, including other resources related to energy or ecological concerns. Regarding population data, this report refers to the recent set of data on population development provided by the authors in the Supplementary Information of reference [3]. This set was created by compiling population data from various sources and subsequently applying numerical filtering based on the Savitzky–Golay principle. It is worth noting that the discussion in the given report includes the years 2023 and 2024, which are not included in refs. [2,3,4].

This report revisits the analytical reasoning that extends the standard Malthusian and Verhulst models towards the so-called super-Malthusian and Verhulst-type models. It incorporates distortion-sensitive and derivative-based analyses, which were recently introduced [2,3,4]. These results are further explored in the given report, focusing on the significance of food resources and the broader concept of carrying capacity.

In light of the expectations and demands of the ongoing Fifth Industrial Revolution era, this paper further discusses the need for food with health-promoting properties and the requirements of a sustainable society and a circular economy. These demands are exemplified by high-pressure preservation and processing (HPP) technology, which uniquely meets these expectations.

3. Results

3.1. Global Population, Carrying Capacity, and Condorcet Criterion

The 17th century was a time when the scientific method was taking shape, laying the conceptual foundations for the Industrial Revolution era that was about to emerge. It emphasized the importance of observations, critical analysis, hypothesis formulation, conducting experimental verifications, and, finally, coherent output data discussion using scaling equations, as well as drawing critical conclusions [64,65,66]. Isaac Newton’s significant contributions to the universal recognition of the scientific method cannot be overstated. He used it to discover the universal laws of nature, which are expressed by functional scaling equations. Examples include the laws of dynamics and the law of gravity in physics. The latter links seemingly distant phenomena, such as an apple falling from a tree and the movements of planets or comets in the sky. Newton also introduced differential analysis to demonstrate model assumptions in depth and the significance of scaling equations [66].

In 1798, Thomas Malthus directly recalled Isaak Newton’s legacy when introducing the first analytic model describing human population growth ($P\left(t\right))$ [67]:

$${\displaystyle \frac{dP\left(t\right)}{dt}}=rP\left(t\right)\Rightarrow G_P\left(t\right)={\displaystyle \frac{1}{P\left(t\right)}}{\displaystyle \frac{dP\left(t\right)}{dt}}={\displaystyle \frac{dlnP\left(t\right)}{dt}}=r$$

(2)

$$P\left(t\right)=P_{0}exp\left(rt\right)$$

(3)

where $r=const$ is the Malthus growth rate parameter, $t$ is the time since the onset of the Anthropocene, and the prefactor $P_0$ is related to $t=0$. Note the introduction of the relaxation time $\tau =1/r$ in refs [2,3].

The left side of Equation (2) recalls the basic work of Malthus [67]. The right side recalls the concept of the relative growth rate (RGR,$G_P$), which was recently discussed [3,4].

Malthus also stressed the meaning of the available food resource amount $F\left(t\right)$ for population growth. It was introduced via a supplementary equation [67]:

$$F\left(t\right)=A+Bt$$

(4)

Considering the interplay of Equations (3) and (4), Malthus concluded [67], ‘The population increases in a geometrical ratio, and the subsistence rises only linearly, which finally leads to ‘times of vice and misery’. This yields the famous Malthus trap (catastrophe), where the quantity of food becomes increasingly insufficient for the growing population. Malthus advised that population constraints or an increase in subsistence (food) would help to escape this trap [67]. Unfortunately, a simplistic escape concept, as in the conquest of other countries, has often been implemented [68,69,70].

A few decades later, Pierre François Verhulst (1838) introduced a model in which food requirements are explicitly included in the scaling equations [71]:

$${\displaystyle \frac{dP\left(t\right)}{dt}}=rP-s{P}^2\Rightarrow G_P={\displaystyle \frac{1}{P\left(t\right)}}{\displaystyle \frac{dP\left(t\right)}{dt}}=r-sP=r\times \left({\displaystyle \frac{K-P\left(t\right)}{K}}\right)$$

(5)

$$P\left(t\right)={\displaystyle \frac{1}{1+Cexp\left(-rt\right)}}$$

(6)

where the parameter $C=1/P_0-s$; $s$ is the Verhulst parameter showing the impact of the necessary resources—originally food—and the carrying capacity: $K=s/r$.

The left-hand parts of Equation (5) are intricately linked to the original Verhulst model formulation [71], marking a significant milestone in our understanding of population dynamics. The right part shows the reformulation exploring the RGR parameter, as proposed recently [3]. It also includes the carrying capacity factor ($K$), introduced by Pearl and Reed [72,73] as a metric for available food, and other necessary resources: from energy to those related to ecological capacities. Following Equation (5), the carrying capacity parameter $K$ can be interpreted as the maximal population in a given system, which is allowed for all available ‘resources’ [3].

Equation (6), derived from Equation (5), is the Verhulst model population portrayal equation, a versatile tool that directly parameterizes population growth. Its adaptability to different systems, particularly in biology, is a testament to its utility in population studies.

A comparison of Equations (2) and (5) indicates that one can consider the apparent growth rate $r^{\prime }\left(r,t\right)=r\left(1-P\left(t\right)/K\right)$. For the Verhulst model, this shows the following: (i) $P\left(t\right)$ first follows the Malthus pattern (Equations (2) and (3)); (ii) next, a continuous decrease in the apparent growth rate $r’$ occurs; finally, (iii) a stationary phase related to $r^{\prime }\left(r,t\right)\to 0$ and $P\left(t\right)\to K$ occurs. The appearance of the apparent Malthus and stationary ‘phases’ led to the name ‘ bimodal behavior’ for the Verhulst equation [74,75].

Note that the behavior discussed above applies to systems with a constant amount of resources (food) despite population growth. This means that resources, including food, are renewable up to a given system’s equilibrium level. For systems with non-renewable resources, the amount of food and resources decreases as the population rises. In such a case, $P\left(t\right)$ reaches a maximum and, subsequently, the population diminishes, down to the ‘death phase’ [7,8].

There are numerous population growth models, which are discussed in detail in references [2,3,4,74,75,76,77,78,79,80,81,82,83,84,85]. In this report, we focus on the Malthusian and Verhulstian scalings, which remain significant references in population studies [86,87,88,89,90,91,92,93,94]. Thomas Malthus’s 1798 model predicts that population growth will outpace resource growth, leading to a crisis. Malthus [67], super-Malthus [2], and Verhulst-type [3,71] models enable us to address the impact of food resources on population dynamics. Their extension yields a unique opportunity for distortion-sensitive analysis, detecting local $P\left(t\right)$ changes, as recently considered by the authors [2,3,4].

Figure 1 presents the global population evolution since the onset of the Anthropocene. It is based on data recently developed by the authors [2,3]. The plot explores a semi-log scale, for which basic Malthusian behavior is visualized as a linear dependence: $lnP\left(t\right)=ln{P}_0+rt=ln{P}_0+\left(1/\tau \right)t$ and ${log}_{10}P\left(t\right)\approx 0.434lnP\left(t\right)$. Note the explicit indication of subsequent historical periods in Figure 1.

The plot reveals the simple Malthus behavior over the vast period of the first nine millennia from the onset of the Anthropocene. For such a pattern, the global population follows simple ‘geometric’ growth, as described by Equations (2) and (3). This could also indicate mean no food restrictions during this period, as discussed in relation to the Malthus and Verhulst models above. The Malthusian growth is accelerated by approximately 4.5 times on passing the crossover from the Early to the Late Neolithic epoch. It is manifested by a change in the slope of the lines in Figure 1. Notably, this occurred soon after the Doggerland flood and the formation of the North Sea [95]. It was accompanied by a rise in sea levels, the further retreat of ice sheet remnants, and climate warming.

Furthermore, Figure 1 shows that this behavior persists even beyond the Bronze Age, encompassing the periods of the first great civilizations in Ancient Egypt, the Middle East, the Mediterranean, China, and India.

Significant irregularities in $P\left(t\right)$ changes appear in Antiquity. This should not be linked to food shortages. This was the time of the formation of great empires, of which the Roman Empire remains the most impactful and memorable. Up to one-third of the global population lived in the Empire for ~500 years, from Julius Caesar’s era to the fall of the Western Roman Empire [96,97]. This might suggest that the ‘stationary phase’ was reached in the Verhulst model scaling, related to the limited availability of food. However, the authors believe that there may be a different, unique reason for such an unusual pattern of $P\left(t\right)$ changes in human history. The Empire’s economy was primarily based on exploiting slaves as a ‘human energy source’, covering an enormous scale. For example, in the giant silver mines in the La Tinto region (present-day Spain), tens of thousands of slaves worked, and their average survival period was only $~3\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{s}$ [97,98].

The Empire’s weakening and its ‘barbarian’ neighbors’ civilizational progress could have effectively limited the ‘supply’ of this ‘enslaved human raw material’, which was so cruelly exploited.

The global population began to grow again after the fall of the Roman Empire.

Starting with the advent of Medieval times, permanent population growth becomes visible, as shown in Figure 1. To highlight the emerging non-linear pattern, the super-Malthus (SM2) relation with the time-dependent growth rate $r\left(t\right)$ and/or the apparent relaxation time $\tau \left(T\right)$ was proposed [2]:

$$P\left(t\right)=P_{0}exp\left(r\left(t\right)\times t\right)=P_{0}exp\left({\displaystyle \frac{t}{\tau \left(t\right)}}\right)\Rightarrow \tau \left(t\right)=t\times ln\left({\displaystyle \frac{P_0}{P\left(t\right)}}\right)$$

(7)

The right-hand side of the above equation shows the transformation that enables the calculation of $\tau \left(t\right)$ changes when $P\left(t\right)$ data are available.

It is notable that, for $r\left(t\right)=r=const$, the SM relation simplifies to the basic Malthus Equation (3). The unique feature of the SM2 relation is the time-dependent relaxation time, $\tau \left(t\right)=1/r\left(t\right)$. This magnitude, commonly used to test dynamics in physics [12,13,14], enables a direct estimation of the time required for a 50% change from the population at a given moment, namely $t_{1/2}=\tau \times ln2$. Nevertheless, the direct parameterization of $P\left(t\right)$ changes via this SM Equation (7) (left part) can be challenging, since it requires prior knowledge of $r\left(t\right)$ or $\tau \left(t\right)$ evolutions.

However, one can apply the above SM relation to calculate temporal changes in the apparent relaxation time, as shown in the right-hand part of Equation (7). The evolution of this magnitude is presented in Figure 2. For such a plot, the horizontal line is related to the basic Malthus Equation (3), with $r\left(t\right)=r=const$, or, alternatively, $\tau \left(t\right)=\tau =const$. Such behavior emerged in the Middle Ages (~1100), lasting until the onset of the Enlightenment period (~1700), with a distortion coinciding with the impact of the Black Death [2,3,4]. The extension of this ‘distortion’ into the 16th century can be related to the enormous population catastrophe in South America resulting from the Spanish Conquest.

From the year ~1710 to the present, the unique linear $\tau \left(t\right)=a-bt$ is visible, as in Figure 2. Substituting this into the SM2 Equation (7), one obtains a relation resembling the constrained critical scaling equation shown on the right-hand side of Equation (1). This issue is discussed in detail in references [2,3].

How did food resources and their availability influence population development during the period considered in Figure 2?

Generally, such a discussion over a long period can be challenging due to significant changes in civilization, cultural diversity, wars, and conquests. However, the Malthus-type trend for the first period, as indicated in Figure 2 (1100–1719), suggests that there was no essential food availability problem on a global scale, in line with the above discussion regarding the Malthus and Verhulst models. Of course, numerous famines and local population catastrophes are known, but their global impacts appeared to be relatively weak.

A possible measure of food availability could be the standardized income of a well-defined but relatively large group of employees, in a country where such distortive factors as wars, conquest, changes in borders, or population flows are negligible. Such conditions can be considered in England, where almost constant earnings among building workers from $~1200$ to $~1840$ are evidenced. A systematic increase in earnings is observed from the mid-19th century onwards [99,100,101]. This could suggest a large ‘rent of benefits’ for industrialists in the First Industrial Revolution, since the enormous increase in productivity had a negligible impact on real wages. Their real value had remained almost unchanged since the Middle Ages.

The Verhulst model approach might seem beyond the global population growth pattern shown in Figure 1. However, one may consider a Verhulst-type equation associated with a set of $(r,s)$ associated with crossing subsequent barriers, occurring well before approaching the stationary phase. The effective portrayal of global population data since the onset of the Anthropocene was considered by Lehman et al. [102], who linked the crossover of subsequent eco- and bio-barriers. The problems and challenges of such an approach were further discussed in ref. [3]. Furthermore, it is worth recalling the report by Cohen [79], who suggested that the basic Verhulst model dependence (Equations (5) and (6)) can indicate a functional link between population growth and the carrying capacity ($K)$ (a metric for available resources). He named this the Condorcet equation [79]:

$${\displaystyle \frac{dK\left(t\right)}{dt}}=c\left(t\right){\displaystyle \frac{dP\left(t\right)}{dt}}=\left({\displaystyle \frac{L}{P\left(t\right)}}\right){\displaystyle \frac{dP\left(t\right)}{dt}}\Rightarrow$$

$$\Rightarrow {\displaystyle \frac{dK\left(t\right)}{dt}}=L{\displaystyle \frac{dlnP\left(t\right)}{dt}}=L{G}_P\left(P,t\right)=L^{\prime }exp\left(bP\right)$$

(8)

where the coefficient $L$ = const.

The first part of Equation (8) is the basic Condorcet equation formulation introduced by Cohen [79]. It includes the suggested ‘dilution’ of the carrying capacity metric by the rising population via the assumption $c\left(t\right)=L/P\left(t\right)$, where $L=const$ [79]. Cohen also suggested that the parameter $L$ can be a measure of the total available resources.

The second part of Equation (8) is the development of the Condorcet equation proposed in this report. It explores the general functional link $dP/P=dlnP$ and the recent finding of the analytic per capita global growth rate (RGR) $G_P$, including its exponential parameterization [2,3]. It opens the door to the direct estimation of carrying capacity evolution through an integrated analysis.

Recalling the above dependencies, and starting from$c=1$, the parameter decreases in each subsequent time $t$, i.e., $c<1$. Finally, it equals$c=0$, yielding the Verhulst model’s stationary state. For $c<0$, the carrying capacity, food resources, and, consequently, the population diminish. When $c>1,$ each additional person in the population increases the system’s carrying capacity beyond their own needs, thus yielding conditions that accelerate population growth, even up to infinity. Here, Cohen [79] attempted to establish a connection to von Foerster et al.’s Doomsday equation, which suggests an infinite global population in 2026 [76]. When published in 1960, this offered a simple scaling equation for $P\left(t\right)$ changes since 400 BCE [76]. However, this scaling failed as more data became available, especially regarding the hypothetical Doomsday in 2026 [2,3,74,75].

Cohen, in ref. [79], offered an inspiring heuristic picture, expressed via Equation (8–first part) and by introducing the Condorcet parameter $c$, which can change in subsequent stages of global population growth. A further development is offered by Equation (8–second part), as discussed above. Furthermore, one can recall the authors’ recent report [3], which discuss the per capita global population rate (RGR), introduced in ref. [102], by introducing its analytic counterpart: $G_P\left(t,P\right)=\left(1/P\right)\left(dP/dt\right)$ [3,4]. Following this, the analysis that directly resulted from the Verhulst model reference derivative Equation (5), explored via the plotting of $G_P\left(t,P\right)$ vs. $P$, revealed significant inconsistencies between the basic Verhulst model expectations and ‘empirical’ global population data [3,4]. This led to the following ‘empowered’ super-Malthus (SM1) equation [2,3]:

$$P\left(t\right)=P_{0}exp{\left(t/\tau \right)}^{\beta }$$

(9)

where the relaxation time $\tau =const$, and $\beta$ is the power exponent characterizing the emergence of the distribution of relaxation times; it also includes the growth rate r = 1/τ and can show the tendency for energy loss and gain in the system via the value of the power exponent. For $\beta =1$, related to a single relaxation time/growth rate, the basic Malthus behavior is retrieved.

In refs. [2,3], distortion-sensitive, derivative-based analysis was directly applied to discrete ‘empirical’ $P\left(t\right)$ data to test subtle local temporal changes. In the recent ref. [3], a link to the per capita relative growth rate (RGR, $G_P$) was discussed.

This provided insights into a subtle ‘upward’ discrepancy from the general trend visible in Figure 2, which occurred after 1965.

It has also been shown that, in the Industrial Revolution era, the following behavior took place: from $~1710$ to $~1965$–$1968$, $\beta >1$; later, up to the present, $\beta <1$. At the indicated crossover, the transition from $\beta \approx 1.5$. to $\beta \approx 0.85$ took place [2,3,4]. This unique crossover is even more strongly manifested for $G_P\left(P\right)$ changes, linking it to the global population $P\left(t\right)~3\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{o}\mathrm{n}$ [3,4]. Notably, the empowered exponential behavior is relatively typical for complex physical systems, where the exponent $\beta >1$ is related to ‘amplified’ development, associated with ‘ordered nucleation centers’ and ‘internal energy’ creation. The stretched exponential case $\beta <1$ is related to multichannel energy dissipation and is observed in predominantly disordered systems [2].

Considering these, we can further reformulate the basic Cohen’s Condorcet relation by implementing the RGR factor for the empowered exponential SM1 Equation (9):

$${\displaystyle \frac{dK\left(t\right)}{dt}}=L{\displaystyle \frac{dP\left(t\right)/P\left(t\right)}{dt}}=L{\displaystyle \frac{dlnP\left(t\right)}{dt}}=L{G}_P\left(t\right)={\displaystyle \frac{L\beta }{\tau }}{\left({\displaystyle \frac{t}{\tau }}\right)}^{\beta -1}$$

(10)

Notably, the right-hand part of the above relation correlates with the so-called hazard rate of the Weibull distribution for a complex system dynamics [2].

The above discussion facilitates an examination of the global (planetary) carrying capacity necessary for the development of the global population based on the values of exponent $\beta$ [2]. Over the millennia, until $~1700,$ the dominant pattern can be related to the exponent $\beta =1$. This means that both the population and resources increased ‘geometrically’, according to the simplest scaling relation of the Malthus model (Equations (2) and (3)). This may indicate that, from the Neolithic period to the onset of the Enlightenment, globally, the most crucial resource was food, and each new member of the global population introduced as many new resources as he/she needed to the system. The ‘disruption’ in $P\left(t\right)$ changes in Antiquity is described above and in ref. [2].

Since the onset of the Industrial Revolution, the ‘accelerated’ population growth, following the Condorcet relation, has been associated with an increased carrying capacity, with parameters $L\mathrm{a}\mathrm{n}\mathrm{d}\beta >1$. During this unique period, groundbreaking technological innovations addressed problems that could have hindered further development, particularly due to the scarcity of resources, energy, and food. Scientific and technological breakthroughs enabled the exploitation of previously unexploited raw materials, significantly increasing the global carrying capacity. An example is the First Industrial Revolution period, namely the Steam Age. It was first driven by wood as an energy source, until large areas of Europe were deforested. The massive exploitation of ‘black coal’ in mines solved this problem. When this appeared to be insufficient for new applications and the growing population, the use of oil and electricity as an energy source emerged as a solution. This has gained importance since the late-19th century. However, it also increased the demand for coal as the essential raw material for electricity generation. Following the crossover that occurred between 1965 and 1968, the global population growth rate shifted towards the pattern predicted by the Condorcet-related parameters $L,\beta <1$. This could reflect a spontaneous reaction of the global population to the impact of constraints on a planetary scale. In the last few decades, the world has become a ‘global village’, and immediate contact between any two places on Earth has become possible. There appears to be a tangible limitation in available space due to the impact of emerging planetary-scale borders. The consequences of violating ecological constraints on a massive scale are global warming and pollution, with global-scale impacts. The response to these formidable challenges, perhaps the most ‘critical’ in human history, is the most significant task of the Fifth Industrial Revolution.

Note that, in Appendix A.1, issues related to subsequent Industrial Revolution periods are briefly presented.

The Fifth Industrial Revolution is currently underway [23,24]. It is most often defined descriptively as a period incorporating the concepts of (i) economic and environmental sustainability, (ii) human-centeredness, and (iii) concern for the environment, matched with artificial intelligence (AI) development. This is a descriptive definition, differing from the earlier stages of the IR, where dominant breakthrough technologies and/or scientific innovations were explicitly addressed. However, the term ‘sustainability’ seems to include issues (ii) and (iii).

The definition of the 5th Industrial Revolution as ‘sustainable development via new generation energy sources, material engineering, and AI implementation’ could better align with the earlier IR periods.

Although the successive stages of the Industrial Revolution era opened up new ‘raw material’ resources or ‘carrying capacity’ [3,79] without considering the dominant food resource, it remained critically important, and its growth was also driven by technological progress. This involved implementing new technologies in agriculture and food production, as well as innovative food preservation methods to ensure product health and safety, addressing the significant challenge of increasingly complex logistics due to the rapidly growing population.

This period also saw the discovery and mass implementation of new food preservation and processing methods. Of particular importance here were the discoveries of Louis Pasteur [31], who identified the microbiological sources of health hazards in food or beverages, related to the presence of pathogenic bacteria, fungi, or yeast, and introduced a means to reduce these hazards to a safe level by heating to a temperature of $~85°\mathrm{C}$ [32]. Then, various chemical preservatives were added to products [33], in parallel cooling and freezing methods were developed [34], and radiation treatments were discovered and implemented [35,36]. Therefore, the response to the significant challenge of rapid population growth was characteristic of the New Brave World [103] of the Industrial Revolution era—namely, the mass implementation of innovative technologies.

Nowadays, the food problem may appear to have been solved globally. Supermarket shelves show an unprecedented assortment of foodstuffs at prices accessible to the ‘average’ consumer. However, this success in food availability also has a ‘dark side’. New methods of food preservation and processing have been identified as a contributing factor to global-scale pandemic threats. They can be considered a significant cause of colossal food waste, reaching $>40\%$ globally [49,50,51].

Reducing this figure is the simplest and most environmentally beneficial way to increase the food supply, aligning with the rise in multi-aspect carrying capacity.

During the Industrial Revolution era, the essential response to emerging, potentially destructive challenges is the development and implementation of breakthrough technologies [23,24,25,26,27,28]. Below, we present the current state of the art and emerging possibilities to solve the food quality challenge and create high-quality foods with explicit pro-health properties and pro-environment features.

High-pressure preservation/processing (HPP) food technology is of exceptional importance and could be a groundbreaking innovation here. This is discussed in the next section. This method has already undergone global market verification and could be essential in increasing the carrying capacity associated with the amount of available food. However, HPP is also associated with pro-health, high-quality foods. Therefore, it is also essential in increasing the social carrying capacity, as it improves the well-being of societies. It encompasses the aforementioned pro-health features, as well as the beneficial environmental impacts resulting from qualitative waste limitations and reduced energy processing demands. Implementing HPP technology can support the fundamental goals of a sustainable and circular economy.

Today, high-pressure preservation/processing (HPP) is referred to as ‘cold’ pressure-assisted pasteurization [5,7,8,52,53,54,55,56,57,58,59,60,61,62,63]. However, the next breakthrough in the implementation of high pressure may be high-pressure sterilization (HPS). This report highlights existing solutions for this emerging innovation, as well as the new generation of colossal barocaloric effect-assisted HPS and HPP concepts, following the authors’ recent proposal [7,8].

3.2. High-Pressure Preservation/Processing of Food

As early as the Middle Pleistocene, pre-humans began preparing food using fire [104,105]. This innovative breakthrough enhanced digestibility and reduced the risk of contamination and pathogens, thereby positively impacting overall health. In addition, it enabled food to be consumed over a longer period, which remains an essential objective of food preservation methods to this day. In subsequent times, increasingly complex methods appeared. These included fumigation and then pre-smoking [104,105]. Then, methods utilizing natural environmental conditions, such as low temperatures (freezing) or wind and low humidity (pre-freeze-drying), were probably used [106]. Subsequently, in the Anthropocene, more complex methods of food preservation emerged, often altering the form of food. For milk, this included sour milk, yogurt, butter, buttermilk, or cheese, for which records appear from as early as $~7000\mathrm{B}\mathrm{C}\mathrm{E}$ [106,107,108]. Then, pickling and marinating using salt and honey (sugar) emerged. Increasingly complex recipes were also developed for the long-term use of meat in the form of ham or sausages [108]. This was the result of implementing ‘innovative technologies’ developed via trial-and-error approaches and the skills of generations of cooks. This massive set of products has shaped today’s cuisine, and they can be included in the category of ‘high-quality foods’, as long as natural products are used.

The Industrial Revolution began only two centuries ago. During this time, the global population has increased from $~600\mathrm{m}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{o}\mathrm{n}$ to $~8.3\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{o}\mathrm{n}$. It has also been a time of previously unknown growth in agricultural productivity, resulting from the implementation of broadly understood technological, biotechnological, and socioeconomic innovations. On a global scale, a significant surplus of food has emerged, manifested by the previously unknown abundance and variety of products in most countries’ stores. Numerous massive urban centers have emerged in response to the implementation of new technologies. For this ‘New Brave World’, the supply of food, in adequate quantities and at least acceptable quality, has become a particularly significant task. In addition to the direct increase in agricultural production, it has become essential to extend products’ shelf lives and safety in increasingly complex logistics conditions. There has also been an increasing range of new and highly processed food products. This has led to the need for a new generation of food preservation methods that ensure the health and safety of the product with a minimal impact on its native form. They include thermal pasteurization and sterilization, a wide range of chemical preservatives, cooling, and freezing [32,33,34,35,36,37,38]. These methods, which date back to the 19th century, are essential factors in the current ‘abundance’ of food. However, their widespread implementation has led to new and serious problems on a global scale [38,39,40,41,42,43,44,45,46]:

✓

Thermal pasteurization ensures microbiological safety, but, at the same time, it often reduces the nutritional quality, vitamin content, and bioactivity.

✓

Chemical additives appear to be directly related to obesity, some types of cancer, allergies, skin problems, and intestinal problems;

✓

Cooling and freezing are excellent preservation methods; however, the use of technological solutions can contribute to global warming;

✓

Irradiation can effectively extend shelf lives and improve safety by killing pathogens and insects; however, there are problems related to nutrient degradation and changes in taste and texture. Therefore, it must be limited to dry products such as spices.

Nowadays, there are expectations for the implementation of innovative food preservation methods based on new, previously unused physical bases. Examples include technologies based on (i) ultrasound, using micro-scale cavitation; (ii) pulsed electric field (PEF) impacts, where the perforation of cell membranes is essential; (iii) fast deep cooling, which is surface-related; (iv) ‘cold’ plasma surface action; and (v) ultraviolet surface action.

Reviews of innovative methods for food preservation can be found in numerous reports [7,50,51,52,61,63].

However, none of these methods is characterized by the particularly desirable ‘universality’— i.e., effects on both liquid and solid products in their entire volumes, the definitive avoidance of chemical preservatives (including salt and sugar), or the uncompromised preservation of the fresh product’s quality over an extended time period. Such a set of preferred features is only achieved by the action of high pressure on food products. This is an innovative method that has already undergone a successful global market test. High-pressure preservation (HPP) technology, implemented for over the last three decades, has positive impacts on the product without the above negative impacts [7,8,52,53,54,55,56,57,58,59,60,61,62,63]. These include the following:

• shelf-life extension of up to 180 days;
• high microbiological safety;
• maintenance of the fresh product’s taste, flavor, and texture;
• maintenance of the fresh product’s vitamin composition;
• maintenance of the bioactive and nutritional properties;
• no chemical preservatives;
• activation/deactivation of selected enzymes;
• salt- and sugar-limited/-free products;
• suitability for ‘fluid’ and ‘solid’ foods;
• application to packaged food, reducing the risk of secondary contamination;
• environmentally friendly technology, namely with (i) limited requirements for electric energy, (ii) an almost complete lack of waste during processing, and (iii) a reduction in the quantity of ‘expired products’ and then the disposal problems;
• ‘clean labels’ and innovative technology.

HPP technology is related to the impact of high pressures, such as $P=300-600\mathrm{M}\mathrm{P}\mathrm{a}$ for $3-15$ min, generally at room temperature.

Figure 3 shows a pilot-scale HPP facility with a pressure chamber with volume $V=50\mathrm{L}$, operating at pressures up to $P=600\mathrm{M}\mathrm{P}\mathrm{a}$.

The image presents the main pressure chamber body and the automated system for the closing and opening of the chamber, as well as the loading of the product. The pressure is supplied from an external high-pressure, large-volume pump. The computerized system is controlled from a panel in an adjacent, safety-isolated room. The HPP processor was designed and built by the ‘UnipressEquipment’ department at IHPP PAS. It is approximately one-third lighter than similar standard processors, which significantly impacts the price and use of ‘critical resources’. It also allows for the more flexible design of the hall in which the processor is placed. The equipment is also fitted with an innovative opening and closing system.

Figure 4 illustrates the conceptual basis of HPP technology, showing an elliptical curve in the pressure–temperature ($P-T$) plane that describes the limits of protein denaturation. The first point, for the atmospheric pressure, on this curve was observed by Louis Pasteur (1863) [31], which gave rise to the technology for the thermal pasteurization of food. It involves reaching the denaturation limit (‘clumping’) of protein structures, which occurs at a temperature of $~85°\mathrm{C}$. Such thermal treatment of the product leads to the denaturation of proteins in the pathogenic organisms present, extending from worms to microorganisms. Today, the denaturation curve is associated with a $\left({10}^{-5}\right)$ reduction in the number of microorganisms [32]. When presented on a logarithmic scale, the term ‘5-log reduction’ is used.

The next point in the above curve can be linked to Percy W. Bridgeman’s compression of egg albumin under room temperature [109,110]. Smeller and Heremans plotted denaturation via modeling, recalling the Clausius–Clapeyron equation, implemented for the given process [111,112,113,114,115,116]:

$${\displaystyle \frac{d{T}_D}{dP}}=T_D{\displaystyle \frac{\Delta V}{L}}={\displaystyle \frac{\Delta V}{\Delta S}}$$

(11)

where $T_D$ is the denaturation temperature at the given pressure, and $L,\Delta V,\Delta S$ are the latent heat, volume change, and entropy change when passing the $T_D\left(P\right)$ curve.

In ref. [116], the elliptic curve was obtained by assuming the pressure-dependent evolution of $T_D\left(P\right)$, $\Delta V\left(P\right)$, $\Delta S\left(P\right)$. It is worth recalling that the Clausius–Clapeyron equation was essentially introduced for the melting–freezing discontinuous transition, i.e., $T_m\left(P\right)$ [111,112,113]. Thus, one can state that Smeller and Heremans [115,116] considered denaturation as a specific discontinuous phase transition. Notably, HPP technology, which is essentially the pressure counterpart of pasteurization, does not act effectively on viruses, for which a significant impact is observed at pressures above 1 GPa. Such high compression is generally destructive to a product and also hazardous and inconvenient in applications [7,117].

Figure 4. The denaturation curve in the pressure–temperature ($P-T$) plane, following refs. [115,116]. The structures of native and denatured proteins are shown. Links to the work of Louis Pasteur (thermal pasteurization under atmospheric pressure) [31] and Percy W. Bridgman (the first denaturation under isothermal compression using egg white) [109,110] are provided. Note the images of these researchers and the dates of their major discoveries in this field (see the text). The vertical grey arrow shows the standard HPP ‘cold pasteurization’ implementation path [7]. The red and blue arrows illustrate the implementation paths for basic CBE-assisted HPP [7,8] and reversed CBE-assisted HPP, respectively. The process first follows path (1). The slope of the arrows is the result of temperature changes via adiabatic compression. Furthermore, the temperature change due to pressure-induced CBE is indicated by path (2). Finally, after passing the denaturation curve, i.e., the target of the process, the decompression occurs, It causes the return to the initial state, as indicated by the dashed arrows (3). Basic CBE-supported HPP is related to pasteurization or sterilization, involving compression and heating. The inverse, CBE-supported HPP is related to compression and cooling.

Figure 4. The denaturation curve in the pressure–temperature ($P-T$) plane, following refs. [115,116]. The structures of native and denatured proteins are shown. Links to the work of Louis Pasteur (thermal pasteurization under atmospheric pressure) [31] and Percy W. Bridgman (the first denaturation under isothermal compression using egg white) [109,110] are provided. Note the images of these researchers and the dates of their major discoveries in this field (see the text). The vertical grey arrow shows the standard HPP ‘cold pasteurization’ implementation path [7]. The red and blue arrows illustrate the implementation paths for basic CBE-assisted HPP [7,8] and reversed CBE-assisted HPP, respectively. The process first follows path (1). The slope of the arrows is the result of temperature changes via adiabatic compression. Furthermore, the temperature change due to pressure-induced CBE is indicated by path (2). Finally, after passing the denaturation curve, i.e., the target of the process, the decompression occurs, It causes the return to the initial state, as indicated by the dashed arrows (3). Basic CBE-supported HPP is related to pasteurization or sterilization, involving compression and heating. The inverse, CBE-supported HPP is related to compression and cooling.

The vertical arrows in Figure 4 show standard paths related to HPP technology. Most often, it is related to near-room-temperature compression, but, generally, operations in the range of $~4°\mathrm{C}$ to $~50°\mathrm{C}$ are considered.

The effect of pressure on food and unwanted microorganisms is more complex than in thermal pasteurization, which is related solely to the denaturation of proteins. At room temperature, compression to $300-400\mathrm{M}\mathrm{P}\mathrm{a}$ usually first causes the rupture of the cell membranes surrounding microorganisms and/or the organelles inside, associated with relatively weak infrastructural interactions. This is the most commonly used mechanism in HPP technology for food preservation. It leads to a 3–5-times (3–5 log) reduction in pathogenic microorganisms while maintaining the unique advantages of this technology, as listed above [7,52]. An example is the thermal pasteurization of milk, which produces a product with a distinct taste from raw milk and, unfortunately, reduced nutritional value. ‘Cold’ pressure pasteurization at room temperature, with compression to $~400\mathrm{M}\mathrm{P}\mathrm{a}$, yields pasteurized milk with the taste and nutritional advantages of ‘native’ milk. Compressing milk to ~600 MPa, which is associated with reaching the denaturation curve, followed by decompression, results in a greater reduction in the number of microorganisms but also a change in taste and a decrease in bionutritional value [7,52].

Thermal pasteurization, which is commonly used today, significantly reduces, but does not eliminate, unwanted pathogenic microorganisms. A pasteurized product, therefore, has a naturally limited shelf life related to microbiological safety.

For many food products, ‘technological’ sterilization is used [32], which consists of heating the product for the shortest possible time—optimally a few/a dozen seconds—to temperatures in the range of $120-150°\mathrm{C}$. This is not the ‘total’ sterilization, which requires much higher temperatures and longer exposition times. It is used, for example, in medicine. However, the mentioned pattern of sterilization applied to food allows for the extension of the product’s shelf life, which reaches a year or more. It is also possible to ‘support’ this shelf life through a minimal addition of chemical preservatives or ensuring an appropriate pH in the product [32].

Note, Appendix A.2 further describes the unique phenomenon of the colossal barocaloric effect, proposed as the supporting conceptual base for the new generation of HPP.

3.3. Compression-Related Sterilization

Sterilization with the support of high pressure is a challenging issue for HPP processors on both pilot and industrial scales (see Figure 3). At present, it is often referred to as pressure-assisted thermal sterilization (PATS), which is typically characterized by temperatures of 121 °C or higher matched with compressing up to ~600 MPa. While such conditions are relatively simple to achieve in laboratory-scale experiments, they are extremely difficult for large-scale industrial or pilot high-pressure processing (HPP) systems. Only recently, a commercial solution to this challenge has been proposed [118]. First, the food product is heated up to $~90°\mathrm{C}$ and then located into a thermally insulated container to create adiabatic conditions. Next, it is moved to the high-pressure chamber, where compression to $P~600\mathrm{M}\mathrm{P}\mathrm{a}$ takes place. This yields adiabatic compression conditions, which leads to a change in the product’s internal energy and, consequently, an increase in temperature, up to $~30°\mathrm{C}$. The product under pressure reaches an effective temperature of $~120°\mathrm{C}$, and, after $5-15$minutes under P ~ 600 MPa, decompression occurs. It lowers its temperature again to $~90°\mathrm{C}$, and then the product is removed from the chamber [118].

For such a l concept, significantly deeper ‘sterilization’ should be expected than with the standard thermal procedure described above. However, for such ‘pressure-assisted sterilization’ technology, the product is exposed to high temperatures for a prolonged period. Together with the compression and decompression time in the high-pressure chamber, this can be several dozen minutes. Therefore, a significant reduction in nutritional value and bioactivity is likely to occur. This is no longer mild HPP technology, such as ‘cold pressure’ pasteurization, as discussed above.

Recently, the authors of this report have presented two innovative concepts that aim to mitigate or even eliminate the disadvantages mentioned above, offering promise for pressure-assisted sterilization with ‘mild-impact’ features [7,8]. This involves the so-called colossal barocaloric effect (CBE) [119,120,121], recently discovered in materials from the soft matter family—particularly those that form a plastic crystalline phase. A strongly discontinuous phase transition, described by the Clausius–Clapeyron relation (Equation (10)), is characterized by colossal latent heat and entropy change values. In adiabatic conditions (thermally insulated containers), in the standard situation of the system where the melting temperature $d{T}_m/dP>0$, this means the release of heat into the interior of the adiabatic container, when the discontinuous melting/freezing transition is passed on compressing. As a result, there is a substantial increase in temperature in the container where the element containing the material exhibiting the CBE phenomenon is placed. Upon decompression, there is an immediate corresponding decrease in temperature. This process is illustrated in Figure 4, which features arrows indicating the subsequent stages of innovative CBE-assisted compression-related sterilization. There are also soft matter systems with a strongly discontinuous phase transition, where compression decreases the transition temperature, i.e., they are related to $d{T}_m/dP<0$ conditions. This is the basis of the inverse barocaloric effect [122,123]. For such systems, compression causes the absorption of heat energy from the environment under adiabatic conditions, which means a decrease in temperature. Decompression means the release of heat to the environment when passing the $T_m\left(P\right)$ curve of discontinuous phase transitions, as well as an increase in the temperature of the surroundings. Such a ‘reversed CBE’ process creates a unique possibility to cross the $T_D\left(P\right)$ denaturation line when the temperature is reduced and, therefore, a new type of ‘truly cold’ pasteurization or sterilization of food. The stages of this process are shown by arrows in Figure 4.

This concept of ‘very cold’ reversed CBE-supported HPP pasteurization and sterilization (arrows in blue, Figure 4) was introduced for the first time in the given report. Note that it is driven only by pressure changes, without supplementary heating as in the standard PATS concept, implemented so far.

A feasibility analysis of CBE-assisted HPP solutions is given in refs. [7,8]. Notably, they offer a precisely controlled process, determined solely by the applied pressure value, with a time-dependent, limited temperature impact (high or low). It can be relatively easily implemented in existing HPP industrial-scale processors. For product operations, a significant aspect is that the product introduced to the chamber can be at near-room temperature, and it remains the same when the product is removed from the chamber.

4. Discussion

Twelve thousand years ago, the Anthropocene began. Thanks to increasingly favorable climatic conditions, Homo sapiens gained extraordinary development opportunities. Humans exhibit a strong inclination towards multidimensional, mutual interactions. Consequently, as with any non-homogeneous complex system characterized in this manner, one can expect the spontaneous emergence of ‘heterogenic structures’, which, in this case, can only mean organized clusters of people. Recent discoveries at Göbekli Tepe and Çatalhöyük (present-day Turkey) have revealed surprisingly large and highly developed quasi-urban centers that can be dated back to ~9000 BCE [124,125].

In both the Neolithic era and today, the most important goal of any individual is to provide food for themselves and their family. The answer to the question of how these needs were shaped in the Anthropocene—the ‘era’ of humans—is complex and ambiguous due to variable geographical, climatic, and cultural conditions. However, such an answer could be indirectly deduced from the appropriate scaling and description of global population changes.

This issue is discussed in the first part of this paper from the perspective of Malthus [67], Verhulst [71], super-Malthusian extension modeling [2,3], and the concept of the carrying capacity introduced by Pearl and Reed [72,73]. Attention is drawn to its use via the ‘Condorcet’ relation concept, proposed by Cohen (1995) [79], which links the carrying capacity with global population changes. In this report, the extension of this relation is proposed, utilizing the results of the authors’ recent work, which enable the direct estimation of the Condorcet coefficient metric with the support of the super-Malthusian description [2,3,4]. The presented analysis indicates that, from the beginning of the Anthropocene to the end of the 17th century, the simple geometric growth of the global population dominated, although with a variable time constant ($r,\tau$) (different periods). Disturbances appeared in ancient times or during the Black Death period. They are commented on in refs. [2,3,4] and above in the given report.

The analysis using the ‘Condorcet model’ suggests that the resources (food) needed for Malthus-type growth increase at the same rate as the population. We wish to highlight new issues related to this topic—specifically, those associated with Equations (8b) and (10)—as well as the related discussion.

Two centuries ago, an extraordinary acceleration in global population growth began. Despite this boost, no Malthusian catastrophe or general global food shortage occurred. On the contrary, a type of food surplus occurred. Moreover, food prices began to fall, and employment in agriculture was reduced even below 10% of the total number of employees in many countries. It is a new era of Industrial Revolutions [23,24]. For the first time in history, massively implemented breakthrough inventions and technologies, supported by modern science and based on the conceptual and philosophical basis of the scientific method, have solved civilizational challenges [64,65,66]. This would not have been possible without feedback interactions with the subsequently implemented ‘socioeconomic innovations’, which changed societies worldwide.

At that time, the carrying capacity ceased to be dominated by food. Additionally, raw materials and energy sources became increasingly important for the ‘technology’ of the subsequent Industrial Revolution periods. There were also massive impacts of resources rarely considered in earlier eras, i.e., shortages of raw materials, energy, or pollution, which have permanently devastated the planet, its climate, and the biosphere. The discussions in recent reports [2,3,4,7,8], as briefly recalled above, show that the complex system of the global population has been spontaneously sensing and reacting to this existential problem since the mid-1960s.

However, the current abundance of the most important resource for humans—food—might be illusory. It is mainly based on food preservation methods that have a devastating effect on society. There is also an unfavorable connection with popular, highly processed food, referred to as ‘junk food’.

It is possible to address these civilizational challenges within the broader context of the Industrial Revolution era—specifically, the development and implementation of innovative technologies.

This paper presents the basics of high-pressure preservation/processing (HPP) technology. The currently existing version of high-pressure ‘cold’ pasteurization has already passed the market validation test. The market for HPP products is worth USD ~600 million, based on several hundred industrial-scale HPP processors and the industry offering solutions in this area [126]. The characteristics of products after HPP processing exhibit surprising alignment between customer and producer needs, namely the quality of a fresh product without preservatives and with extended durability. Inherent waste reduction is important for the environment, as is minimizing disposal costs. There is also the possibility to extend this technology, i.e., pressure-assisted sterilization, with support from the CBE concept, as discussed above and in references [7,8]. We would like to emphasize the difference between this concept and the pressure-assisted sterilization (PATS) approach that has been used until now [52,57,61,62]. Standard PAST implementation in large-volume pressure chambers remains a significant challenge. The first solution in this area was only implemented recently [118]. In such a context, high-pressure processing supported by CBE (CBE-HPP), related to ‘deep’ pasteurization or sterilization, could open up new possibilities: (i) the process is controlled solely by pressure changes; (ii) it is possible to reduce the time of the synergistic action of temperature and pressure; (iii) as with standard HPP technology, significant energy is only supplied during the short compression period, which reduces the electricity requirements considerably; and (iv) the reversed colossal barocaloric effect opens up new possibilities by enabling processing under pressure at low temperatures—see this report and refs. [7,8].

In recent decades, other new generations of methods for food and beverage preservation have been developed:

(i)

pulsed electric fields (PEFs) [127];

(ii)

ultrasound [128];

(iii)

supercritical fluid domains (SCFDs) [129];

(iv)

ultraviolet radiation [130];

(v)

cold plasma ionized gases [131];

(vi)

intense, spectrum-selected pulsed light [132];

(vii)

packing via atmosphere and/or nanoparticles embedded in polymer films [133,134].

These methods have significant functionality that is already being exploited, but their application is limited to some specific features or foods. For example, they are focused on liquids and thin, near-surface product layers, and there are implementation difficulties for both ‘solid’ and ‘liquid’ products. Sterilization is not possible, and achieving the defined pasteurization level (5-log decay) may require repeated and relatively lengthy applications.

High-pressure processing generally has no such limitations, and the new generation of high-pressure sterilization methods offers possibilities that are unavailable with other methods. However, HPP methods are currently limited by the relatively high initial costs and complexity of the high-pressure processors, which additionally require well-qualified personnel for support. Notwithstanding, the current generation of HPP processors is designed to last for at least 100,000 cycles, and the price of the base device is expected to decrease over time. For example, the processor shown in Figure 3 features a pressure chamber that is one-third lighter than the current standard. This results in a lower price, the reduced use of valuable raw materials, and lower requirements for the hall where the processor is assembled.

5. Conclusions

The global population is a model system that is spatially limited on a planetary scale. It has developed thanks to its internal interactive dynamics and the fundamental support of available resources within the system. A specific metric for these resources is the concept of the carrying capacity, which defines the maximum amount that can be sustainably exploited by the population. The current era is unique because civilization has expanded to a planetary scale. This results in universally felt spatial limitations, global environmental threats, and cultural unification. In this new world, food still remains the most critical resource. Today, as in the past, the goal of every human being is to adequately secure food for themselves and their family. Nowadays, however, there are expectations not only regarding the quantitative satisfaction of ‘energy needs’ but also regarding health-promoting effects or, at the very least, the absence of harmful effects. Therefore, it is expected that sufficient quantities of high-quality, preferably health-supporting foods will be obtained and processed in a way that minimizes harmful environmental and social impacts before being provided to consumers.

The first part of this report discusses the concept of the carrying capacity and how it can be estimated from global evolutionary changes, based on the Condorcet equation introduced by Cohen [3,8,79]. The discussion is then expanded further to derive explicit functional relationships using the super-Malthusian description recently introduced by the authors of this paper [2,3].

The importance of innovative food preservation and processing methods is demonstrated, as these can significantly increase the supply of high-quality food, extend product freshness, and impart new, targeted health benefits. Attention is drawn to the dominant role of high-pressure technologies, including high-pressure preservation and processing (HPP)—particularly the newly emerging capabilities of CBE-supported high-pressure sterilization. The challenge remains to further improve the design of HPP processors, reducing their weight and simplifying their construction to extend their maintenance-free lifespan and price. Such progress could result in the widespread availability of high-quality foods, which are expected by societies currently developing sustainable civilizations. It would support the expansion of local products’ availability to at least sub-global markets, which could in turn create a vast number of jobs.

It seems possible to offer food in a system that is ideally in line with the goals of a ‘sustainable society’ and to fulfil the great desire of Hippocrates of Cos (460–375 BCE), the ‘father’ of medicine: ‘Let food be thy medicine and medicine be thy food’ [135]. Altogether, this could result in a significant increase in the carrying capacity of the modern world.