Неравновесная термодинамика: принципы и особенности

Branch of thermodynamics

Non equilibrium thermodynamics is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities (non equilibrium state variables) that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions. Almost all systems found in nature are not in thermodynamic equilibrium, for they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems and to chemical reactions. Many systems and processes can, however, be considered to be in equilibrium locally, thus allowing description by currently known equilibrium thermodynamics. Nevertheless, some natural systems and processes remain beyond the scope of equilibrium thermodynamic methods due to the existence of non variational dynamics, where the concept of free energy is lost. The thermodynamic study of non equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. One fundamental difference between equilibrium thermodynamics and non equilibrium thermodynamics lies in the behaviour of inhomogeneous systems, which require for their study knowledge of rates of reaction which are not considered in equilibrium thermodynamics of homogeneous systems. This is discussed below. Another fundamental and very important difference is the difficulty, in defining entropy at an instant of time in macroscopic terms for systems not in thermodynamic equilibrium. However, it can be done locally, and the macroscopic entropy will then be given by the integral of the locally defined entropy density. It has been found that many systems far outside global equilibrium still obey the concept of local equilibrium.

A profound difference separates equilibrium from non equilibrium thermodynamics. Equilibrium thermodynamics ignores the time courses of physical processes. In contrast, non equilibrium thermodynamics attempts to describe their time courses in continuous detail. Equilibrium thermodynamics restricts its considerations to processes that have initial and final states of thermodynamic equilibrium; the time courses of processes are deliberately ignored. Non equilibrium thermodynamics, on the other hand, attempting to describe continuous time courses, needs its state variables to have a very close connection with those of equilibrium thermodynamics. This conceptual issue is overcome under the assumption of local equilibrium, which entails that the relationships that hold between macroscopic state variables at equilibrium hold locally, also outside equilibrium. There are, however, situations where there are appreciable non linear effects even at the local scale.

Some concepts of particular importance for non equilibrium thermodynamics include time rate of dissipation of energy (Rayleigh 1873, Onsager 1931, also), time rate of entropy production (Onsager 1931), dissipative structure, There are other approaches to non equilibrium thermodynamics, for example extended irreversible thermodynamics, but they are hardly touched on in the present article.

According to Wildt (see also Essex), current versions of non equilibrium thermodynamics ignore radiant heat; they can do so because they refer to laboratory quantities of matter under laboratory conditions with temperatures well below those of stars. At laboratory temperatures, in laboratory quantities of matter, thermal radiation is weak and can be practically nearly ignored. But, for example, atmospheric physics is concerned with large amounts of matter, occupying cubic kilometers, that, taken as a whole, are not within the range of laboratory quantities; then thermal radiation cannot be ignored.

The terms 'classical irreversible thermodynamics' for systems. In some writings, it is assumed that the intensive variables of equilibrium thermodynamics are sufficient as the independent variables for the task (such variables are considered to have no 'memory', and do not show hysteresis); in particular, local flow intensive variables are not admitted as independent variables; local flows are considered as dependent on quasi static local intensive variables. Also it is assumed that the local entropy density is the same function of the other local intensive variables as in equilibrium; this is called the local thermodynamic equilibrium assumption (see also Keizer (1987)). Radiation is ignored because it is transfer of energy between regions, which can be remote from one another. In the classical irreversible thermodynamic approach, there is allowed spatial variation from infinitesimal volume element to adjacent infinitesimal volume element, but it is assumed that the global entropy of the system can be found by simple spatial integration of the local entropy density. This approach assumes spatial and temporal continuity and even differentiability of locally defined intensive variables such as temperature and internal energy density. While these demands may appear severely constrictive, it has been found that the assumptions of local equilibrium hold for a wide variety of systems, including reacting interfaces, on the surfaces of catalysts, in confined systems such as zeolites, under temperature gradients as large as K m, and even in shock fronts moving at up to six times the speed of sound. In other writings, local flow variables are considered; these might be considered as classical by analogy with the time invariant long term time averages of flows produced by endlessly repeated cyclic processes; examples with flows are in the thermoelectric phenomena known as the Seebeck and the Peltier effects, considered by Kelvin in the nineteenth century and by Lars Onsager in the twentieth. These effects occur at metal junctions, which were originally effectively treated as two dimensional surfaces, with no spatial volume, and no spatial variation.

A further extension of local equilibrium thermodynamics is to allow that materials may have "memory", so that their constitutive equations depend not only on present values but also on past values of local equilibrium variables. Thus time comes into the picture more deeply than for time dependent local equilibrium thermodynamics with memoryless materials, but fluxes are not independent variables of state.

Extended irreversible thermodynamics is a branch of non equilibrium thermodynamics that goes outside the restriction to the local equilibrium hypothesis. The space of state variables is enlarged by including the fluxes of mass, momentum and energy and eventually higher order fluxes. The formalism is well suited for describing high frequency processes and small length scales materials.

In thermodynamics one is often interested in a stationary state of a process, allowing that the stationary state include the occurrence of unpredictable and experimentally unreproducible fluctuations in the state of the system. The fluctuations are due to the system's internal sub processes and to exchange of matter or energy with the system's surroundings that create the constraints that define the process. If the stationary state of the process is stable, then the unreproducible fluctuations involve local transient decreases of entropy. The reproducible response of the system is then to increase the entropy back to its maximum by irreversible processes: the fluctuation cannot be reproduced with a significant level of probability. Fluctuations about stable stationary states are extremely small except near critical points (Kondepudi and Prigogine 1998, page 323). The stable stationary state has a local maximum of entropy and is locally the most reproducible state of the system. There are theorems about the irreversible dissipation of fluctuations. Here 'local' means local with respect to the abstract space of thermodynamic coordinates of state of the system. If the stationary state is unstable, then any fluctuation will almost surely trigger the virtually explosive departure of the system from the unstable stationary state. This can be accompanied by increased export of entropy.

The scope of present day non equilibrium thermodynamics does not cover all physical processes. A condition for the validity of many studies in non equilibrium thermodynamics of matter is that they deal with what is known as local thermodynamic equilibrium.

Local thermodynamic equilibrium of matter The longer relaxation time is of the order of magnitude of times taken for the macroscopic dynamical structure of the system to change. The shorter is of the order of magnitude of times taken for a single 'cell' to reach local thermodynamic equilibrium. If these two relaxation times are not well separated, then the classical non equilibrium thermodynamical concept of local thermodynamic equilibrium loses its meaning He defined 'local thermodynamic equilibrium' in a 'cell' by requiring that it macroscopically absorb and spontaneously emit radiation as if it were in radiative equilibrium in a cavity at the temperature of the matter of the 'cell'. Then it strictly obeys Kirchhoff's law of equality of radiative emissivity and absorptivity, with a black body source function. The key to local thermodynamic equilibrium here is that the rate of collisions of ponderable matter particles such as molecules should far exceed the rates of creation and annihilation of photons.

It is pointed out by W. T. Grandy Jr, that entropy, though it may be defined for a non equilibrium system is—when strictly considered—only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under special circumstances, however, one can metaphorically think as if the thermal variables behaved like local physical forces. The approximation that constitutes classical irreversible thermodynamics is built on this metaphoric thinking. This point of view shares many points in common with the concept and the use of entropy in continuum thermomechanics, which evolved completely independently of statistical mechanics and maximum entropy principles.

Non equilibrium thermodynamics has been successfully applied to describe biological processes such as protein folding/unfolding and transport through membranes. It is also used to give a description of the dynamics of nanoparticles, which can be out of equilibrium in systems where catalysis and electrochemical conversion is involved. Also, ideas from non equilibrium thermodynamics and the informatic theory of entropy have been adapted to describe general economic systems.