Non-equilibrium Phenomena

A section of Entropy (ISSN 1099-4300).

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The field of non-equilibrium phenomena is growing in interest day by day; in fact, one may argue that almost any observable macroscopic phenomenon occurs in non-equilibrium conditions. To make any sense, this statement requires a definition of equilibrium, the status that must be violated for non-equilibrium to be established. In this respect, one notes that there are very many notions of equilibrium. Remaining within the realm of physics, and of thermodynamics in particular, the most relevant equilibria are the following: mechanical equilibrium (material objects remain at rest, subjected to no net forces); chemical equilibrium (the composition of an extended body does not change in time, and hence, possible chemical reactions are balanced, and no net transport of mass takes place); thermal equilibrium (the object of interest does not change its state if isolated from its environment). When concomitant, these three equilibria give rise to thermodynamic equilibrium. From a microscopic point of view, the conditions for thermodynamic equilibrium include that the elementary constituents of the objects of interest are very many, and that they interact so that atomic or molecular properties be rapidly homogenized in space. There are various degrees in which these conditions can be violated, but it is obvious that a vast range of phenomena, particularly of interest in present science and technology, do not fit the definition of thermodynamic equilibrium and call for specific approaches.

While non-equilibrium thermodynamics and statistical mechanics border and partially overlap with numerous aspects of equilibrium statistical physics and thermodynamics, because they share a large fraction of notions and terminology, rather different techniques have been developed to specifically treat non-equilibrium phenomena.

In general, statistical physics is a subject in which determinism and randomness, probabilities, and rigorous laws relating to material properties of macroscopic objects are finely intertwined, and since its origins, it is devoted to understanding thermodynamics. Its techniques are so successful that it is applied also to non-macroscopic objects, and to phenomena outside of the physical and natural realm. One feature of the equilibrium cases is that dissipation does not play a relevant role, entropy being the main quantity of interest. By contrast, energy dissipation is one of the main features of non-equilibrium systems and extends well beyond the domain of entropy. Dissipation requires specific tools to be treated.

Thermodynamics has a clear and wide range of applicability to equilibrium phenomena that occur even relatively far from the scale of our daily life. It is among the most robust theories of physics, and we do not expect that new evidence will require modifications of any of its basic tenets in the foreseeable future. Without thermodynamics, our technology would simply not be available. It remains confined to equilibrium states, possibly relating different states that may be obtained one from another by means of some transformation in time, and it does not really treat the associated dynamics. Non-equilibrium thermodynamics, on the other hand, concerns systems for which global equilibrium does not hold, but that can be subdivided in parts each of which is like a small thermodynamic equilibrium system. Although apparently close, it has developed numerous techniques that depart from those of equilibrium thermodynamics. Such techniques are required, in particular, to treat dissipation.

Consequently, the mathematical formalism and the observable quantities of interest in the study of non-equilibrium phenomena are usually quite different from those of statistical mechanics and thermodynamics. At the same time, the investigation of non-equilibrium phenomena is much less settled than that of equilibrium phenomena, and a unifying framework, while present in the equilibrium case, is missing in the non-equilibrium case. This is also due to the variety of non-equilibrium phenomena, which hugely exceeds that of equilibrium phenomena. For each equilibrium phenomenon, there are very many different ways of perturbing it and of obtaining a non-equilibrium phenomenon. The result is that quite different approaches, including discrete as well as continuous models, and stochastic as well as deterministic models, have been developed to treat different cases. This makes it hard to find the key that suits them all. At present, dissipation and fluctuations have become ubiquitous buzz words, apparently capable of leading to some kind of unitary picture, but much more progress is required and much progress expected in the years to come.

All that has a reflection in the foundations of physics. Non-equilibrium phenomena are among the most prolific sources of questions about physical theories, their meaning, and their applicability, ranging from the microscopic realm to the cosmological one. Recently, even an original approach to machine learning and artificial intelligence has arisen within the framework of non-equilibrium phenomena, which impacts on foundations of various other disciplines, beyond physics.

This Section collects original research papers, papers on applications in technology and science at large, and papers presenting original perspectives and reviews of well-established subjects. Submissions addressing novel issues, as well as those on more specific topics are welcome.

Prof. Dr. Lamberto Rondoni
Section Editor-in-Chief

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