Thermodynamics with Internal State Variables

1967/07/15 by Bernard D. Coleman, Morton E. Gurtin · 1,781 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Computer science #Differential equation #Dissipation #Elasticity and Material Modeling #Internal energy #Internal heating #Mathematical analysis #Mathematics #Mechanics #Nonlinear system #Ordinary differential equation #Physics #Quantum mechanics #Stability (learning theory) #State (computer science) #State variable #Statistical physics #Thermodynamics #Thermoelastic and Magnetoelastic Phenomena

paper · doi:10.1063/1.1711937

published in The Journal of Chemical Physics 47(2), 597-613 (American Institute of Physics)

openalex publication_date 1967/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

This is a study of the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations. After employing a method developed by Coleman and Noll to find the general restrictions which the Clausius—Duhem inequality places on response functions, we analyze various types of dynamical stability that can be exhibited by solutions of the internal evolution equations. We also discuss integral dissipation inequalities, conditions under which temperatures can be associated with internal states, and the forms taken by response functions when the material is a fluid.

Citations

• Thermodynamics and departures from Fourier's law of heat conduction
• Thermodynamics of materials with memory
• The thermodynamics of elastic materials with heat conduction and viscosity

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