The dynamics of thermodynamics

Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation for isolated systems does not allow one to say too much about thermodynamic properties in non-equilibrium conditions. From there on, the notion of quasi-isolated systems is introduced, for which it is possible to describe the state of macroscopic systems by a collection of intensive variables. The latter are the differentials of the entropy with respect to the given set of extensive constraints. Arguments are developed showing that the dynamics of irreversible relaxation of non-equilibrium systems consists of two qualitatively different steps. The theory is applied and verified by describing transport processes and calculating the corresponding coefficients. Structure formation and transition to turbulence are equally formalized in the thermodynamic framework.
Comment: 43 pages revtex, 2 figures. Presented at the Workshop on Time-Reversal Symmetry in Dynamical systems, Warwick, U.K., 9th-20th December 1996