A virtual dissipation principle and Lagrangian equations in non-linear irreversible thermodynamics

Abstract

Abstract. — A principle of virtual dissipation is derived which genera¬ lizes d'Alembert's principle to non-linear irreversible thermodynamics, leading to a corresponding Hamiltonian form and Lagrangian equations. It constitutes the fundamental mathematical tool for the analysis of general non-linear dissipative physical systems by methods similar to those of classical mechanics. The principle provides a derivation of the differential field equations or the Lagrangian equations which govern any particular dissipative thermodynamic system and is not based on a priori knowledge of the field equations. Results are essentially an ultimate development of the author's earlier work originated in 1954 which was presented in a more restricted context.