Entropy Principle Exploited by Lagrange Multipliers

Synonyms

Entropy inequality; Lagrange multipliers; Second sound; Simple mixtures

Definition

A proper thermodynamic theory of mixtures avoids the so-called paradox of diffusion, by which disturbances in concentration propagate at infinite speeds. A theory with equations of balance of momenta for the constituents does that. Constraints on the constitutive functions are implied by the entropy principle which is exploited by use of Lagrange multipliers.

Introduction

The entropy principle provides restrictions on the form of the constitutive functions in thermodynamics. And Lagrange multipliers are a convenient tool for the exploitation of such restrictions. The method is illustrated here for a mixture of inviscid fluids – a paradigmatic case.

The basis for a systematic theory of mixtures was laid down by Truesdell (1957), and Müller has developed its thermodynamics in several papers (Müller, 1968, 1973; Müller and Villaggio, 1976), the latter in collaboration with Villaggio. Those were...