# Economies Evolve by Energy Dispersal

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## Abstract

**:**

^{nd}law of thermodynamics. The universal law, when formulated locally as an equation of motion, reveals that a growing economy develops functional machinery and organizes hierarchically in such a way as to tend to equalize energy density differences within the economy and in respect to the surroundings it is open to. Diverse economic activities result in flows of energy that will preferentially channel along the most steeply descending paths, leveling a non-Euclidean free energy landscape. This principle of ‘maximal energy dispersal’, equivalent to the maximal rate of entropy production, gives rise to economic laws and regularities. The law of diminishing returns follows from the diminishing free energy while the relation between supply and demand displays a quest for a balance among interdependent energy densities. Economic evolution is dissipative motion where the driving forces and energy flows are inseparable from each other. When there are multiple degrees of freedom, economic growth and decline are inherently impossible to forecast in detail. Namely, trajectories of an evolving economy are non-integrable, i.e. unpredictable in detail because a decision by a player will affect also future decisions of other players. We propose that decision making is ultimately about choosing from various actions those that would reduce most effectively subjectively perceived energy gradients.

## 1. Introduction

^{nd}law of thermodynamics, which was recently formulated as an equation of motion for natural processes [6,7,8]. In this form, evolution by natural selection can be recognized as being guided by the 2

^{nd}law. This relationship is in agreement with earlier reasoning about the governing role of the 2

^{nd}law, known also as the principle of increasing entropy, in directing numerous natural processes, animate as well as inanimate [9,10,11,12,13,14,15,16,17,18].

^{nd}law but are actually manifestations of it. The entropy of an entire economic system does not decrease due to its diverse activities at the expense of entropy increase in its surroundings. Rather, it follows from the conservation of energy that both the economy and its surroundings are increasing in entropy (decreasing in available energy) when mutual differences in energy densities are leveling off as a result of economic activity. The key here is that according to the statistical physics of open systems increasing entropy means dispersal of energy, rather than as increasing disorder. Finally, we understand the ultimate motivation of economic activities, not as the maximizing of profit or productivity, but rather to disperse energy.

^{nd}law is found to yield functional structures, hierarchical organizations, skewed distributions and sigmoid cumulative curves that also characterize economies. Here, we use the thermodynamic formalism to address some fundamental questions of economics. What drives economic growth and diversification? Where do the law of diminishing returns, the Pareto principle, the balance of supply and demand, and the principle of comparative advantage come from? Why is it so difficult to predict economic growth and decline?

^{nd}law, when formulated properly using the statistical physics of open systems, reveals that nature is an intrinsically interdependent system and its evolution is inherently a non-deterministic process. Thus, our holistic account aims to remove doubts and concerns commonly leveled against physicalism. Yet, our objective is not to turn economics into physics, but to clarify economic activity in the context of the 2

^{nd}law, which accounts for all irreversible motions in nature.

## 2. Economy as an Energy Transduction System

_{j}that result from production activities are indexed by j. They are made from various raw materials or semi-finished products available in numbers N

_{k}. Agricultural, industrial, logistical, informational, etc., processes that transform N

_{k}to N

_{j}also couple quanta of energy, ΔQ

_{jk}per each unit product. The energy supply may be in various forms including labor which, in terms of physics, is work. Each material entity j, is associated with an energy content denoted by G

_{j}relative to the average energy k

_{B}T of the system per entity. For historical reasons the everyday meaning of ambient temperature T relates via k

_{B}to the average energy density of the geophysical system as sensed by thermometers In the same way body temperature is measure for the average energy density of the biological system. In the same sense the common k

_{B}T is a meaningful concept for a sufficiently statistical economic system where entities interact with each other frequently [41]. In previous studies economic systems have been compared on the basis of the average energy density [42]. A pool of indistinguishable (identical) entities N

_{j}, that are the result of natural processes such as chemical reactions, is a repository of energy denoted by the density ϕ

_{j}= N

_{j}exp(G

_{j}/k

_{B}T) [43].

**Figure 1.**Self-similar description of an economy as an energy transduction system. Each entity is regarded as a system (circle) of its own in interactions (lines and arrows) with its surrounding systems (larger circles). The energy difference Δμ

_{jk}between the j and k system and the external energy flux ΔQ

_{jk}(grey background) that couples to the transformations are the driving forces of economic activities. The energy differences are the forces that generate flows of energy (blue arrows) and propel the economic system toward a thermodynamic stationary state where energy density differences within the system and in respect to its surroundings have leveled, hence there is neither growth or decline. The steady state is maintained by the incessant to-and-fro flows of energy between the system and its surroundings.

_{k}= k

_{B}Tlnϕ

_{k}and μ

_{j}= k

_{B}Tlnϕ

_{j}. When μ

_{k}+ ΔQ

_{jk}> μ

_{j}, more products N

_{j}can be made from the available raw-materials N

_{k}and any input energy ΔQ

_{jk}. On the other hand when μ

_{k}+ ΔQ

_{jk}< μ

_{j}, there is a surplus of products that the economic system would then be searching for ways to reduce. Thus, the free energy, known also as the affinity A

_{jk}= μ

_{k}+ ΔQ

_{jk}– μ

_{j}, is the driving force of economic activities that generate diverse flows of energy in both material forms and radiation, which are in terms of physics scalar and vector potentials.

_{jk}, e.g., work. The total force, when positive (A

_{jk}> 0), makes the production of N

_{j}a probable process (dN

_{j}/dt > 0), i.e., the energy flow is statistically speaking always “downhill”. According to our natural approach, all processes, regardless of being either conscious or unconscious, must follow the law of energy dispersal.

_{j}, are constantly regenerated using surrounding supplies. This leads to incessant circulation of matter in both economic systems and ecosystems. Under these conditions random variation in syntheses or deliberate design of production may yield more effective mechanisms of energy transduction which will be naturally selected by the flows themselves to level the density differences even more effectively.

## 3. Economic Evolution as an Energy Dispersal Process

_{j}, is a product of probabilities so that each P

_{j}is associated with a subsystem composed of entities j in numbers N

_{j}(for the derivation see references [6,8]):

_{j}are themselves also made of various entities k each distinct ingredient available in numbers N

_{k}(Figure 1). The form ΠN

_{k}in the numerator ensures that if any of the k-ingredients is missing, no j-product can be made (P

_{j}= 0). The degeneracy g

_{jk}denotes the number of k-components that remain indistinguishable (symmetric) even after being assembled in the j-product. The energy difference ΔE

_{jk}= ΔG

_{jk}– ΔQ

_{jk}in the production process is bridged by the intrinsic difference ΔG

_{jk}= G

_{j}– G

_{k}between the raw materials and products and by the external influx ΔQ

_{jk}. The division by the factorial N

_{j}! means that the combinatorial configurations of identical N

_{j}in the system are indistinguishable. The nominator is raised to the power of N

_{j}because the production process may combine the raw materials into any of the indistinguishable products.

_{B}lnP. It takes into account all densities of energy and paths of transformations:

_{jk}= Δμ

_{jk}– ΔQ

_{jk}is the motive force that directs the transformations from N

_{k}to N

_{j}. The potential difference Δμ

_{jk}= μ

_{j}– Σμ

_{k}contains co-products and by-products of N

_{j}in Σ

_{k}with the opposite sign. The Stirling’s approximation implies that the system is well-defined by being sufficiently statistical, i.e., A

_{jk}/k

_{B}T << 1 to absorb or emit quanta without a marked change in its average energy density k

_{B}T. Otherwise, if S is not a sufficient statistic for k

_{B}T [41], the embedded entities, e.g. semi-finished products N

_{k}themselves would be transforming rapidly. Obviously then the assembly of N

_{j}would be jeopardized. For example, it would be difficult to build a house from bricks that themselves were still soft and deforming. In such a case, the production process must be analyzed at a lower level of hierarchy [47,48] where the submerged evolutionary processes involving the k-entities, e.g., the fabrication of bricks, would be described using the same self-similar formalism.

_{j}/dN

_{j})(dN

_{j}/dt):

_{j}= dN

_{j}/dt that consume the motive forces A

_{jk}. The population change dN

_{j}and the time step dt have been denoted as continuous only for convenience whereas actual processes advance in quantized steps ΔN

_{j}during Δt.

^{nd}law of thermodynamics in the form of an equation of motion for the overall probability (Equation 3.3) is a powerful description of an evolving economy. Yet, it is not P itself but numerous activities and material flows that are amenable for monitoring the economic state. In a sufficiently statistical system each flow:

_{jk}> 0 to satisfy the continuity v

_{j}= –Σv

_{k}between the density ϕ

_{j}and diverse densities ϕ

_{k}[6,49].

_{jk}/k

_{B}T << 1 of being a sufficiently statistical system is assumed but it is not unusual that the assumption does not hold. This critical phenomenon is also familiar from fluid mechanics when a flow changes from laminar to turbulent. When the transformation mechanism σ

_{jk}itself is evolving or when the free energy A

_{jk}is comparable to the average energy density k

_{B}T, the linear relationship between the flow and force (Equation 3.5) fails, but this is no obstacle for the self-similar description. When the condition of being sufficiently statistical is not satisfied at a particular level of hierarchy, the process would need to be described in a finer detail at a level further down in the hierarchy. For example, a series of improvements on a production line will increase the throughput by increasing σ

_{jk}. The time-dependence of the evolving conduction system is fully contained in the recursive, scale-independent system description according to Equations 3.1–3.5.

_{jk}/k

_{B}T << 1 will fail also when energy is not distributed effectively enough within the system to maintain its integrity, i.e. to maintain common k

_{B}T. The economy is subject to disintegration when an economic sector is receiving high influx (or another is draining high efflux). The rapidly growing subsystem acquires greater independence when it is not connected effectively enough to distribute acquired assets to others. Eventually when the high influx ceases, redistribution processes catch up and the excursion for independence ends. The disintegration and reintegration processes are fully contained in the self-similar formalism.

_{jk}(Equation 3.5) drive the flows, not the differences in number densities N

_{j}, which are commonly used in economic [52] as well as in ecological models, e.g., written as sets of coupled differential equations [53]. These models based on the law of mass action [54] erroneously picture that transformation rates would be changing during kinetic courses even when the system is sufficiently statistical. Consequently it may appear as if kinetics was inconsistent with thermodynamics.

_{B}lnP as the law of increasing entropy [6,8]:

_{jk}, are decreasing by way of various flows v

_{j}. The non-negativity of dS/dt is apparent from the quadratic form obtained by inserting Eqaution 3.5 in 3.6. The formula obtained from statistical physics of open systems is consistent with the basic maxim of chemical thermodynamics [45], i.e., the entropy maximum corresponds to the free energy minimum as well as with the classical form of dS given by Carnot [46], the Gouy-Stodola theorem [55,56] and the mathematical foundations of thermodynamics [50,57,58].

_{j}and N

_{k}of energy transduction mechanisms are governed by the mutual energy differences ΔE

_{jk}= ΔG

_{jk}– ΔQ

_{jk}relative to the average energy k

_{B}T per entity in the particular system. The everyday notion of temperature T, when given in units of Kelvin and multiplied with k

_{B}, refers to the average energy of ambient atmospheric gas per molecules that the thermometer is sensitive to. In the same physical sense the average energy density of an economy can be quantified. However, it would extremely tedious to tabulate changes in energy in every transaction. Instead, various economic barometers are used to sense the status of the economic system. The maximum entropy state S

_{max}= k

_{B}ΣN

_{j}

^{ss}, where all energy density differences have vanished, is a dynamic stationary state so that variations ΔN

_{j}about the steady-state populations N

_{j}

^{ss}are rapidly averaged out by economic activities that correspond to conserved flows (ΣΔN

_{j}Δμ

_{jk}= 0). In modern times, apart from some transient periods, economies have not been in stationary states. Instead the average energy influx from the surroundings has been and is still growing due to more and more effective agricultural, industrial, logistical and informational processes [61].

## 4. Origin of Non-Deterministic Economic Evolution

^{nd}law in the form of an equation of motion clarifies the fundamentals that underlie difficulties in providing accurate economic forecasts. The equation of evolution (Equation 3.3), despite being simple, cannot be solved analytically, e.g., integrated in a closed form, because when there are multiple degrees of freedom the variables L and P cannot be separated from each other as they both depend on N

_{j}and A

_{j}. The non-integrable characteristics of the evolving system mean that economic trajectories are non-deterministic. The uncertainty stems from the following factors.

_{k}is in a functional relation to other potentials μ

_{j}via available transformation mechanisms (Figure 1). In a market μ

_{k}can be transformed to μ

_{j}by various transactions, here expressed using numerous flow equations (Equation 3.5), so that the products and other economic entities, just as any other forms of energy, are interdependent. Owing to the continuity v

_{j}= –Σv

_{k}in the transformations it is impossible to change one entity without affecting others. The energy flows v

_{j}and driving forces A

_{jk}are inseparable in L from each other when there are three or more degrees of freedom (agents). Flows affect driving forces that, in turn, affect the flows. A decision taken by a player will change sets of states accessible by other players that, in turn, by their own decisions, affect the sets of accessible states of others. When the currents are not conserved, the ceteris paribus assumption does not hold and the equation of motion cannot be solved by a transformation to yield an analytical formula to determine the system’s time course. Hence evolutionary courses, including economic growth and decline, are non-integrable, i.e. trajectories of an evolving economy cannot be predicted in detail. The problem is exactly the same as was encountered first in the context of the three body problem [62] and later recognized to seed also chaotic behavior [63,64]. The non-deterministic course toward a defined solution–here, the free energy minimum–identifies the problem of predicting economic growth among many other natural processes in computational terms, as non-polynomial time complete [34,65].

_{k}, flows v

_{j}and available jk-transformation paths would not help to estimate the current state and to project toward future states. But the prognoses, even when based on the same premises, will diverge when extended over longer and longer periods of time. Furthermore, it is emphasized that mere information gathering and its exposition are thermodynamic processes themselves that will inevitably affect the course of economy. This has, of course, been understood in practice and regulated by legislation, but has here been associated with the fundamental properties of non-conserved systems with degrees of freedom where forces and flows are inseparable from each other. For example, the use of insider information is prohibited because it would endanger the overall progression by limiting conceivable actions.

## 5. Natural Selection Criterion

_{jk}> 0, consume a common pool of free energy, the magnitudes of flows from the same source via distinct mechanisms distribute according to σ

_{jk}. When a particular mechanism is unable to acquire enough flow from the common resources even for its own regeneration, it will, in biological terms, face extinction as a result of competition. Technological developments alter energy flows and redirect economic growth just as advantageous genetic mutations change the food chain and affect biological evolution. Eventually the most effective paths of economic productivity funnel all flows and leave nothing for the least effective means of energy dispersal, that then ‘run out of business’. This thermodynamic principle for maximal entropy production, equivalent to the maximal energy dispersal, is universal.

^{nd}law, the primary motive of economic activities is the most effective dispersal of energy, whereas it is of secondary importance whether the processes are defined as conscious or unconscious. Therefore, legislation and its enforcement that also consume free energy in redirecting flows and in altering mechanisms, are regarded as natural forces. Also in biological systems natural selection is at work both when particular traits are intentionally sought by breeding and when they appear in response to unintentional forces [1]. The selection between mechanisms by the rate of entropy increase is a particularly stringent criterion when free energy is becoming depleted. This condition is usually referred to as ‘operating on a small margin’. As well, unit costs are reduced by way of voluminous transformations (‘economies of scale’).

_{jk}/k

_{B}T << 1.

**Figure 2.**Simulated evolution of an economy based on the 2

^{nd}law of thermodynamics. Flows, including sporadic variation (up to 10% in the flows), direct down along the steepest gradients of free energy according to Equation 3.5. Entropy (S black line) is increasing as long as the system emerges with novel, increasingly more effective mechanisms of various kinds (j blue line) that are able to acquire more and more energy from the surroundings. When a new mechanism appears, the growth rate increases whereas the stationary state is approached with diminishing returns. During the evolutionary course the distribution that was sampled at various times t (blue bar charts), shifts from simple mechanisms at low-j fractions to sophisticated machinery at high-j fractions. Each fraction is proportional to a population’s effectiveness in energy transduction relative to the others. A catastrophe is introduced at t

_{c}. It demolishes a fraction of the stationary state production capacity (red bars). Consequently, entropy will momentarily plummet as it takes time for the system to recover by restoring the skewed distribution. Scales of axes are in arbitrary units because the simulation is based on scale-independent formalism. See appendix for technical details.

## 6. Evolving Energy Landscape

_{j}, their mutual differences, all transforming flows v

_{j}and all jk-transforming mechanisms. However, to model an economy to the precision of an atom and a quantum is neither practical nor instructive, but coarse-grained simulations of natural processes are easy to set up and execute according to Equation 3.5 [29,30,31,32,33,34,35,36,37].

_{B}T. Time-dependent tangential vectors as directional derivates D

_{j}= (dx

_{j}/dt)(∂/∂x

_{j}) span an energy landscape, properly referred to as an affine manifold, in the continuum limit [7,8,49,74] (Figure 3). Heights of the manifold are high potentials μ

_{k}/k

_{B}T = ln[N

_{k}exp(G

_{k}/k

_{B}T)] at the site x

_{k}and valleys are low potentials μ

_{j}/k

_{B}T = ln[N

_{j}exp(G

_{j}/k

_{B}T)] at x

_{j}. Their difference in the continuum limit is denoted by the gradient –∂U

_{k}/∂x

_{j}and the external energy by the field ∂Q

_{jk}/c∂t in the orthogonal direction denoted (redundantly) by i. The various economic activities generate continuous flows v

_{j}= dx

_{j}/dt from the heights to the valleys. During evolution the landscape is leveling due to numerous flows.

**Figure 3.**Economy is pictured in a self-similar manner as systems within systems (encircled cyclic paths) that are embedded in the surrounding energy landscape. The diverse high-energy densities in the hierarchical organization are associated with transduction mechanisms that direct flows of energy (blue arrows) among themselves and from the surroundings down to the economy. Eventually the landscape may develop to open up for new flows (dashed arrow to right), so that a previously confined steady-state systems will face evolution, e.g., perceived as economic restructuring due to integration.

_{jk}/∂t in the jk-transformations. The external energy (i.e. work) drives the production process in addition to the potential difference between the raw-materials and products. However at a local region, as Gauss noted, the curved landscape can be viewed as nearly Euclidean [8,77]. In other words, to a good approximation the high-density source μ

_{k}does not deplete during the outflow, and the low-density sink μ

_{j}does not fill during the inflow. In economic terms, the Euclidean approximation means that prices of raw-materials and products do not alter during an on-going transaction. In practice, it is of course noticed that, in particular, huge bargains do change the prices of subsequent deals. Contracts aim at predictability but only time-limited offers are given, ultimately because nature is, when depicted as an energy density landscape, inherently non-Euclidean.

## 7. Motives of Integration and Disintegration

_{k}will be in competition with each other [12]. Such a system is not stable according to the Lyapunov criterion [44,64]. This situation, referred to in the biological context as competitive exclusion, may resolve if the units differentiate in respect to each other [80] or one of them disappears, or becomes assimilated to the other in a merger.

^{nd}law (Equation 3.6) subjectivity will be shaped only by perceived proximate gradients. A subsystem supports integration when it gains in dS/dt. Conversely, we propose that a subsystem will tend to break loose when the integration seems to afford a smaller rate of dS/dt than the system could produce independently. How this driving force for integration (or disintegration) actually transpires as flows in any particular system will depend upon available mechanisms. Consistently, it has been proposed that new levels may appear in a dynamical hierarchy only if that results in a more rapid overall energy gradient depletion [81].

## 8. Roots of Economic Relations and Regularities

_{k}(t) + ΔQ

_{jk}– μ

_{j}(t) ≥ 0 per unit time represents profit from the viewpoint of a producer of μ

_{j}. The producer may invest acquired free energy in increasing its production capacity, as well as in obtaining more raw materials and energy, in hopes of maintaining rapid growth to improve its entropy production status. However, eventually, when no new innovations and no supplies are found, the free energy declines. This particular business branch is maturing and its growth is slowing down. Finally, when the free energy vanishes altogether, no more profit can be made, but to make a living is still possible when the market is saturated with products, just as animate populations tend to be in balance in a mature ecosystem.

_{k}(t) + ΔQ

_{jk}– μ

_{j}(t) ≥ 0 that an additional input ΔN

_{k}will give an additional output ΔN

_{j}with diminishing marginal returns. Often this classical law by Ricardo is supplemented with a caveat that only “after a certain point”, the diminishing returns would first set in. This empirical observation of initially increasing marginal products results from the aforementioned initial growth that may be prolonged by restructuring of activities, increasing capacity, efficacy and specializing. As a result of autocatalysis, the initial growth curve is concave and only later becomes convex yielding an overall sigmoid, nearly logistic form [86].

_{k}+ ΔQ

_{jk}= μ

_{j}, the demand and supply are equal, i.e., in balance. For a given supply the increase in consumer demand, denoted by an increase in ΔQ

_{jk}, gives rise to a difference, Σμ

_{k}+ ΔQ

_{jk}> μ

_{j}+ ΔQ

_{jk}´ that is balanced by raising the price denoted by ΔQ

_{jk}´. For a given demand the increase in producer’s supply gives rise to a difference that is balanced by lowering the price, assuming as usual that no other alternatives would open up (Figure 4). The money associated with potential contributes to the transaction motive, just as does the external energy ΔQ

_{jk}. Also a value-added tax, customs, etc., are associated with potentials that influence rates of transformations (Equation 3.5) and affect the market equilibrium (Equation 3.7), and also indirectly when the collected assets are returned to the system. In general a change in a particular commodity price will also affect the demand and supply of other products, and then elasticity behaves non-deterministically. These intractable responses can be simulated using the flow equations Equation 3.5.

**Figure 4.**Demand (black) and supply (blue curve) relate by purchasing power ΔQ

_{jk}and pricing ΔQ

_{jk}´ to the quest for the balance (Equation 3.7) between energy densities ϕ

_{j}and ϕ

_{k}associated with the products (N

_{j}) and raw-materials (N

_{k}).

_{B}T) of an economy that is growing. Obviously, unemployment is reduced during the growth period as the growth is consuming the labor force, literally A

_{jk}. Conversely, a reducing economy faces deflation risk and increasing unemployment.

## 9. Economic Stability, Fluctuations and Oscillations

_{j}in Equation 3.7 depends on its ability to acquire energy from its surroundings relative to all other mechanisms in the same system. For example in a developed economy, characterized by high k

_{B}T, the most abundant fractions associate with median-income households. These dominant fractions of the distribution on a log-log plot follow the power-law, which in the context of incomes, is referred to as the Pareto principle. The low-income fractions associated with the poorest are smaller, as are the high-income fractions of the long tail [90] associated with the richest [91]. The corresponding distribution of a developing economy, characterized by low k

_{B}T, peaks at the lower fractions [92,93]. Usually the income distributions are taken as inequality indicators [94] whereas here insight to the evolving distribution of wealth is drawn from the law of energy dispersal. Earlier these skewed distributions and their cumulative curves viewed as power-laws have been obtained using statistical physics concepts [95], in particular self-similarity in scaling [28], or using Tsallis’ entropy [96], but not explicitly from the 2

^{nd}law, although maximum principles have been understood as being in control [87].

_{jk}/dt = 0). Its isergonic motions, i.e., dynamics on the Euclidean energy landscape, are along statistically predictable trajectories determined solely by the potential and kinetic energy equilibrium condition 2K + U = 0 as the net flux 〈Q〉 = 0. The steady-state kinetic energy to-and-fro flows correspond to commodity exchange without net profit or loss. The stationary state structure-functional diversity, i.e., the maximum entropy partition of energy transduction mechanisms, can be referred to as the Pareto-efficient economy in the context of game theory or as the Nash equilibrium that is maintained by mixed strategy [97]. However, the stationary state is often only evanescent since the surroundings seldom stay invariant for long, and a system will subsequently tend to senesce and become recycled [12].

_{j}according to the Lyapunov criterion δS < 0 and dδS/dt > 0 [44,64]. Any excess or shortage ±δN

_{j}will be soon be abolished by an opposing gradient that drives the reverse flow dN

_{j}/dt and returns the system back to a maximum entropy partition. The same phenomenon is familiar from population fluctuations in ecosystems that are maintained by a steady influx of energy accompanied by a steady thermal outflow. We emphasize that any particular steady state of a dissipative system is stable only against variations in the existing densities and mechanisms, but must adapt to changes in surroundings as well as those imposed by new mechanisms. Variations in production may yield new superior mechanisms to provide access to new resources. Then the system is once again on an evolutionary track. Thus, for any economy, just as for an ecosystem, there is no absolute guaranty of stability. Furthermore, owing to the limited life span of any dissipative system, there are always systems within systems at various developmental phases on their way toward maturity.

_{max}state, stability is naturally sought by all mechanisms. Accordingly, contemporary human endeavors at the global scale aspire after a greater control of increasingly larger surroundings, e.g. by meteorite surveillance and accompanied precautionary measures. These conscious actions aim at contributing to the global homeostasis that has been maintained approximately for eons by biotic means. This proposition was articulated by the Gaia theory [98] and recently shown to follow from the 2

^{nd}Law [33].

_{j}/dt ∝ N

_{j}, into Equation 3.6 we realize that then δS < 0 and also dδS/dt < 0, which means that the Lyapunov stability criterion is violated. Therefore the autocatalytic processes will easily disrupt the balance. When a powerful mechanism appears in an economy, densities associated with raw-materials, semi-finished products, savings etc., will easily become over-depleted by the over-populating products or assets. These self-reinforcing kinetic mechanisms are reasons for intrinsic economic perturbations. For example, energy densities associated with fuels, food supplies, stocks, etc., but represented in modern electronic forms, can be transformed swiftly from one form to another. A rapid accumulation of huge deposits and large deficits signals an imbalance and entails an inevitable restructuring to regain the steady-state partition.

## 10. On Decision Making

_{j})(dN

_{j}/dt) > (dS/dN

_{ĵ})(dN

_{ĵ}/dt). The consumer, as a thermodynamic system, makes decisions among alternatives on a subjective basis about the factors affecting its capability to further entropy production. Also the producer makes decisions based on a subjective view of energy gradients. Each player in the market will prefer a particular series of transformations, usually referred to as a strategy, to move from one state to another higher in entropy production. For this natural reason the views of consumer and producer are not identical but they do not have to be opposite either, rather, more like parallel in a highly integrated economy.

## 11. Discussion

## Supplementary material

Supplementary File 1## Acknowledgements

## Appendix

_{j}/dt using the flow equation Equation 3.5. The starting state of the system is determined by assigning all entities j with initial values N

_{j}, and G

_{j}as well as defining endergonic and exergonic jk-transformations with rates σ

_{jk}. The initial state of the surroundings is defined likewise by the amounts of entities N

_{k}with energies G

_{k}and energy ΔQ

_{jk}that couples to the reactions in the system. The initial free energy terms A

_{jk}are calculated and used to drive the population changes ΔN

_{j}in a step of time Δt. Subsequently all driving forces are updated and used again to drive the next step of population changes. When the step Δt is kept short, the forces will not change abruptly and the system remains sufficiently statistical to be described by a common average energy density k

_{B}T. In this way the simulated evolution advances step by step while entropy (Equation 3.6), as a status measure, is only monitored. The simulation approaches a dynamic stationary state where populations fluctuate about the free energy minimum values. A representative ensemble of non-deterministic process can be obtained by varying the rates σ

_{jk}(randomly).

_{1}(stable entities) and available jk-transformations. When using a PC, a simple brute-force simulation that starts off with 10

^{5}basic building blocks will arrive at a stationary state partition housing 10

^{2}j-classes in overnight. Presumably the convergence can be improved by algorithms that map the free energy landscape and direct the course along optimal descents.

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**MDPI and ACS Style**

Annila, A.; Salthe, S.
Economies Evolve by Energy Dispersal. *Entropy* **2009**, *11*, 606-633.
https://doi.org/10.3390/e11040606

**AMA Style**

Annila A, Salthe S.
Economies Evolve by Energy Dispersal. *Entropy*. 2009; 11(4):606-633.
https://doi.org/10.3390/e11040606

**Chicago/Turabian Style**

Annila, Arto, and Stanley Salthe.
2009. "Economies Evolve by Energy Dispersal" *Entropy* 11, no. 4: 606-633.
https://doi.org/10.3390/e11040606