Nonequilibrium

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 variables (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. It relies on what may be thought of as more or less nearness to thermodynamic equilibrium. Non-equilibrium thermodynamics is a work in progress, not an established edifice. This article will try to sketch some approaches to it and some concepts important for it.

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. Some systems and processes are, however, in a useful sense, near enough to thermodynamic equilibrium to allow description with useful accuracy by currently known non-equilibrium thermodynamics. Nevertheless, many natural systems and processes will always remain far beyond the scope of non-equilibrium thermodynamic methods. This is because of the very small size of atoms, as compared with macroscopic systems.

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 or impossibility in defining entropy at an instant of time in macroscopic terms for systems not in thermodynamic 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. Consequently, equilibrium thermodynamics allows processes that pass through states far from thermodynamic equilibrium, that cannot be described even by the variables admitted for non-equilibrium thermodynamics, such as time rates of change of temperature and pressure. For example, in equilibrium thermodynamics, a process is allowed to include even a violent explosion that cannot be described by non-equilibrium thermodynamics. Equilibrium thermodynamics does, however, for theoretical development, use the idealized concept of the "quasi-static process". A quasi-static process is a conceptual (timeless and physically impossible) smooth mathematical passage along a continuous path of states of thermodynamic equilibrium. It is an exercise in differential geometry rather than a process that could occur in actuality.

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