Search Results (12)

In 1974, Stephen Hawking made the groundbreaking discovery that black holes emit thermal radiation, characterized by a specific temperature now known as the Hawking temperature. While his original derivation is intricate, retrieving the exact expressions for black hole temperature and entropy in a simpler, more intuitive way without losing the core physical principles behind Hawking’s assumptions is possible. This is obtained by employing the Heisenberg Uncertainty Principle, which is known to be connected to thenvacuum fluctuation. This exercise allows us to easily perform more complex calculations involving the effects of quantum gravity. This work aims to answer the following question: Is it possible to reconcile Prigogine’s second law of thermodynamics for open systems and the second law of black hole dynamics with Hawking radiation? Due to quantum gravity effects, the Heisenberg Uncertainty Principle has been extended to the Generalized Uncertainty Principle (GUP) and successively to the Extended Uncertainty Principle (EUP). The expression for the EUP parameter is obtained by conjecturing that Prigogine’s second law of thermodynamics and the second law of black holes are not violated by the Hawking thermal radiation mechanism. The modified expression for the entropy of a Schwarzschild black hole is also derived. Full article

According to the Prigogine–Glansdorff principle, in a thermodynamic system where non-equilibrium processes occur, the change in entropy production is negative or equal to zero. Forest plantations are an example of such thermodynamic systems. Based on the ecological–physiological models of the forest stand growth dynamics developed by the authors of this work, the specific entropy production in the growth of stands was calculated, which is known to be proportional to the entropy production. It is shown that at the age when the minimum value of the specific entropy production is reached, the biomass of the stand has a maximum value. This conclusion is an important predictive factor for practical forestry, since determining the time of the minimum entropy production allows us to determine the time interval at which the biomass of the stand reaches its maximum value. Full article

In this paper, we discuss some well-known experimental observations on self-organization in dissipative systems. The examples range from pure fluid flow, pattern selection in fluid–solid systems to chemical-reaction-induced flocking and aggregation in fluid systems. In each case, self-organization can be seen to be a function of a persistent internal gradient. One goal of this article is to hint at a common theory to explain such phenomena, which often takes the form of the extremum of some thermodynamic quantity, for instance the rate of entropy production. Such variational theories are not new; they have been in existence for decades and gained popularity through the Nobel Prize-winning work of theorists such as Lars Onsager and Ilya Prigogine. The arguments have evolved since then to include systems of higher complexity and for nonlinear systems, though a comprehensive theory remains elusive. The overall attempt is to bring out examples from physics, chemistry, engineering, and biology that reveal deep connections between variational principles in physics and biological, or living systems. There is sufficient evidence to at least raise suspicion that there exists an organization principle common to both living and non-living systems, which deserves deep attention. Full article

How to predict the evolution of ecosystems is one of the numerous questions asked of ecologists by managers and politicians. To answer this we will need to give a scientific definition to concepts like sustainability, integrity, resilience and ecosystem health. This is not an easy task, as modern ecosystem theory exemplifies. Ecosystems show a high degree of complexity, based upon a high number of compartments, interactions and regulations. The last two decades have offered proposals for interpretation of ecosystems within a framework of thermodynamics. The entrance point of such an understanding of ecosystems was delivered more than 50 years ago through Schrödinger’s and Prigogine’s interpretations of living systems as “negentropy feeders” and “dissipative structures”, respectively. Combining these views from the far from equilibrium thermodynamics to traditional classical thermodynamics, and ecology is obviously not going to happen without problems. There seems little reason to doubt that far from equilibrium systems, such as organisms or ecosystems, also have to obey fundamental physical principles such as mass conservation, first and second law of thermodynamics. Both have been applied in ecology since the 1950s and lately the concepts of exergy and entropy have been introduced. Exergy has recently been proposed, from several directions, as a useful indicator of the state, structure and function of the ecosystem. The proposals take two main directions, one concerned with the exergy stored in the ecosystem, the other with the exergy degraded and entropy formation. The implementation of exergy in ecology has often been explained as a translation of the Darwinian principle of “survival of the fittest” into thermodynamics. The fittest ecosystem, being the one able to use and store fluxes of energy and materials in the most efficient manner. The major problem in the transfer to ecology is that thermodynamic properties can only be calculated and not measured. Most of the supportive evidence comes from aquatic ecosystems. Results show that natural and culturally induced changes in the ecosystems, are accompanied by a variations in exergy. In brief, ecological succession is followed by an increase of exergy. This paper aims to describe the state-of-the-art in implementation of thermodynamics into ecology. This includes a brief outline of the history and the derivation of the thermodynamic functions used today. Examples of applications and results achieved up to now are given, and the importance to management laid out. Some suggestions for essential future research agendas of issues that needs resolution are given. Full article

The heat and matter transfer during glucose catabolism in living systems and their relation with entropy production are a challenging subject of the classical thermodynamics applied to biology. In this respect, an analogy between mechanics and thermodynamics has been performed via the definition of the entropy density acceleration expressed by the time derivative of the rate of entropy density and related to heat and matter transfer in minimum living systems. Cells are regarded as open thermodynamic systems that exchange heat and matter resulting from irreversible processes with the intercellular environment. Prigogine’s minimum energy dissipation principle is reformulated using the notion of entropy density acceleration applied to glucose catabolism. It is shown that, for out-of-equilibrium states, the calculated entropy density acceleration for a single cell is finite and negative and approaches as a function of time a zero value at global thermodynamic equilibrium for heat and matter transfer independently of the cell type and the metabolic pathway. These results could be important for a deeper understanding of entropy generation and its correlation with heat transfer in cell biology with special regard to glucose catabolism representing the prototype of irreversible reactions and a crucial metabolic pathway in stem cells and cancer stem cells. Full article

Lactic fermentation and respiration are important metabolic pathways on which life is based. Here, the rate of entropy in a cell associated to fermentation and respiration processes in glucose catabolism of living systems is calculated. This is done for both internal and external heat and matter transport according to a thermodynamic approach based on Prigogine’s formalism. It is shown that the rate of entropy associated to irreversible reactions in fermentation processes is higher than the corresponding one in respiration processes. Instead, this behaviour is reversed for diffusion of chemical species and for heat exchanges. The ratio between the rates of entropy associated to the two metabolic pathways has a space and time dependence for diffusion of chemical species and is invariant for heat and irreversible reactions. In both fermentation and respiration processes studied separately, the total entropy rate tends towards a minimum value fulfilling Prigogine’s minimum dissipation principle and is in accordance with the second principle of thermodynamics. The applications of these results could be important for cancer detection and therapy. Full article

In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These “open Markov processes” serve as the building blocks for more complicated processes. In this paper, we describe the potential application of this framework in the modeling of biological systems as open systems maintained away from equilibrium. We show that non-equilibrium steady states emerge in open systems of this type, even when the rates of the underlying process are such that a detailed balanced equilibrium is permitted. It is shown that these non-equilibrium steady states minimize a quadratic form which we call “dissipation”. In some circumstances, the dissipation is approximately equal to the rate of change of relative entropy plus a correction term. On the other hand, Prigogine’s principle of minimum entropy production generally fails for non-equilibrium steady states. We use a simple model of membrane transport to illustrate these concepts. Full article

The evolution of the entropy production in solids due to heat transfer is usually associated with the Prigogine’s minimum entropy production principle. In this paper, we propose a critical review of the results of Prigogine and some comments on the succeeding literature. We suggest a characterization of the evolution of the entropy production of the system through the generalized Fourier modes, showing that they are the only states with a time independent entropy production. The variational approach and a Lyapunov functional of the temperature, monotonically decreasing with time, are discussed. We describe the analytic properties of the entropy production as a function of time in terms of the generalized Fourier coefficients of the system. Analytical tools are used throughout the paper and numerical examples will support the statements. Full article

Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings). The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress) in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it. Full article

Under which circumstances are variational principles based on entropy production rate useful tools for modeling steady states of electric (gas) discharge systems far from equilibrium? It is first shown how various different approaches, as Steenbeck’s minimum voltage and Prigogine’s minimum entropy production rate principles are related to the maximum entropy production rate principle (MEPP). Secondly, three typical examples are discussed, which provide a certain insight in the structure of the models that are candidates for MEPP application. It is then thirdly argued that MEPP, although not being an exact physical law, may provide reasonable model parameter estimates, provided the constraints contain the relevant (nonlinear) physical effects and the parameters to be determined are related to disregarded weak constraints that affect mainly global entropy production. Finally, it is additionally conjectured that a further reason for the success of MEPP in certain far from equilibrium systems might be based on a hidden linearity of the underlying kinetic equation(s). Full article

The fundamental optimization principle for non-equilibrium thermodynamics is given. The second entropy is introduced as the quantity that is maximised to determine the optimum state of a non-equilibrium system. In contrast, the principles of maximum or minimum dissipation, which have previously been proposed by Onsager, Prigogine, and others as the variational principle for such systems, are shown to be incapable of fulfilling that rôle. Full article

Certain aspects of the history, derivation, and physical application of the information-theoretic entropy concept are discussed. Pre-dating Shannon, the concept is traced back to Pauli. A derivation from first principles is given, without use of approximations. The concept depends on the underlying degree of randomness. In physical applications, this translates to dependence on the experimental apparatus available. An example illustrates how this dependence affects Prigogine's proposal for the use of the Second Law of Thermodynamics as a selection principle for the breaking of time symmetry. The dependence also serves to yield a resolution of the so-called ``Gibbs Paradox.'' Extension of the concept from the discrete to the continuous case is discussed. The usual extension is shown to be dimensionally incorrect. Correction introduces a reference density, leading to the concept of Kullback entropy. Practical relativistic considerations suggest a possible proper reference density. Full article