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A Variational Principle in Thermodynamics

Abstract Offprint We deal with those thermodynamical transport processes in which the current densities are proportional to the gradient of the intensive quantities. We intro­duce a 'potential function' to the intensive quantities so that by its help a Lagran­gian and a variational principle of classical type can be constructed. The ana­logon of the energy momentum tensor, i.e. the thermodynamical tensor, and the canonically conjugated quantities are derived. 1. Introduction The variational principles of thermodynamics so far, exploit the existence of certain dissipation potentials (Onsager [1], De Groot, Mazur [2], Prigogine [3], Gyarmati [4, 5]). One of the most general of these is Gyarmati's variational principle, the Governing Principle of Dissipative Processes (GPDP). It considers the balance equations as subsidiary conditions to the extremum problem. It gives back the constitutive equations as Euler-Lagrange equations, if the coefficient matrix is symmetric