Onsager’s thermodynamic extension

The fundamental question in transport theory is Can one describe processes in nonequilibrium systems with the help of (local) thermodynamic functions of state (thermodynamic variables) This question can only be checked experimentally. On an atomic level, statistical mechanics is the appropriate theory. Since the entropy, 5, is the characteristic function for the formulation of equilibria (in a closed system), the deviation, SS, from the equilibrium value, S0, is the function which we need to use for the description of non-equilibria. Since we are interested in processes (i.e., changes in a system over time), the entropy production rate a = SS is the relevant function in irreversible thermodynamics. Irreversible processes involve linear reactions (rates 55) as well as nonlinear ones. We will be mainly concerned with processes that occur near equilibrium and so we can linearize the kinetic equations. The early development of this theory was mainly due to the Norwegian Lars Onsager. Let us regard the entropy S(a,/3,. ..) as a function of the (extensive) state variables a,/ ,. .. .which are either constant (fi,.. .) or can be controlled and measured (a). In terms of the entropy production rate, we have (9a/0f=a)... 

We have seen how classical thermodynamics may be extended to include fluctuations Boltzmann s eqs. (A.7) and (A.8) being key results of this extension. Onsager, within the context of his linear theory, has generalized Boltzmann s equilibrium fluctuation theory to dynamics. We next briefly discuss this generalization (compare Section II.B.4). 

In summary, Onsager did succeed in finding a nonequilibrium extension of equilibrium thermodynamics. However, to resolve the dual problem of formulating a thermodynamic equation of motion and of choosing the thermodynamic forces, he was obliged to make limiting slow variable assumptions. Thus his central Eq. (A.53) models actual macroscopic parameters motions in a highly simplified way, namely, as coupled diffusive motions in the equilibrium potential oc S Tp A) of Eq. (A.36). 

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