NONLOCAL LAGRANGE FORMALISM IN THE THERMODYNAMICS OF IRREVERSIBLE-PROCESSES - VARIATIONAL PROCEDURES FOR KINETIC-EQUATIONS

This paper is concerned with generalizations of the known local Lagran ge formalism of first order. It will be applied to kinetic equations l ike the Fokker-Planck equation and the Boltzmann equation. In the latt er case nonlocal methods are necessary from the very beginning. Nevert heless, in the framework of Frechet's formalism the calculations are a s easy as in the classical local case. Furthermore, a rather general e ntropy concept can be established within nonlocal Lagrange formalism f or irreversible systems. As a main result of this paper we derive with in our general concept the known entropy balances of the Boltzmann the ory and the Fokker-Planck theory, respectively. It will be emphasized that our general concept may be applied to a very wide class of irreve rsible systems, in principle.