A Kinetic Interpretation of Thermochemical Restrictions of Continua

Abstract: In their seminal work, Rajagopal and Srinivasa established how the second law of thermodynamics, expressed through the Clausius–Duhem inequality, imposes powerful restrictions on the constitutive equations of continua, often allowing one to determine the constitutive relations of a material. This talk explores a kinetic interpretation of such thermochemical restrictions. The analysis of the entropy balance naturally yields a kinetic analogue of the Clausius–Duhem inequality, while the H-theorem provides a microscopic justification of the second law. In the hydrodynamic limit, a Chapman–Enskog expansion demonstrates how the classical constitutive relations of continuum mechanics—such as the Euler equations and the ideal gas law—arise as zeroth-order approximations that maximize entropy production. We hope that this kinetic perspective offers a new interpretation of the thermomechanical restrictions introduced by Rajagopal and collaborators, clarifying their origin within the statistical description of particle systems.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)