Nonequilibrium Thermodynamics of Canonically Invariant Relaxation Processes

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Abstract
A relaxation process in which a dilute system is in weak interaction with a heat bath is termed canonically invariant if the time‐dependent system distribution function maintains its canonical form throughout the relaxation process and is thus characterized by a time‐dependent temperature. We discuss here the nonequilibrium (i.e., time‐dependent) thermodynamics of such canonically invariant relaxation processes. Explicit analytic forms are obtained for the partition functions Q(t), the system thermodynamic properties E(t), A(t), S(t), and Cv(t), the global free energy and entropy a(t) and s(t), and their time derivatives for both classical and quantum systems. For quantum systems with a finite number of discrete energy levels, the above treatment is extended to include canonically invariant processes at negative absolute temperatures. Finally, we demonstrate that an initial canonical distribution for a fixed S(0) extremizes the entropy production of systems exhibiting canonically invariant relaxation processes.