Principles and representations of nonequilibrium thermodynamics

Abstract

A theory treating the space-time structure of nonequilibrium processes is developed. The basis of the theory is founded upon the validity of: (i) the kinetic form of the Gibbs equation and consequently, the generalized thermodynamic potentials, and (ii) the balance equation of entropy, the continuity equation, and the conservation of energy. The dissipation function is derived from the kinetic form of the Gibbs equation. The only additive invariant remaining in nonequilibrium thermodynamics is the energy; within the entropy representation, it can be used to establish a local energy conservation or power equation. The first and second variations of the power equation determine the stationary-state conditions and the stability of the stationary state, respectively. It is impossible to characterize nonequilibrium stationary states in terms of only one generalized thermodynamic potential; a free extremum of the potential does not exist since the stationary-state values of the forces enter in the first variation of the potential. A constrained variational principle of least dissipation of energy is applicable to certain classes of nonequilibrium stationary-states, which may or may not be spatially homogeneous. Distinction is made between variational principles (e.g., least dissipation of energy) and extremum principles (e.g., minimum production of entropy). A kinetic criterion of mechanical equilibrium is derived from the direction of the entropy flux.