The Second Law of Thermodynamics and Stability,
BROWN UNIV PROVIDENCE R I LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
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There are several indications pointing to an intimate relationship between the second law of thermodynamics and stability. Here I attempt to establish a different connection between stability and the second law, in that stability will be interpreted as continuous dependence of thermodynamic processes upon initial state and supply terms. The ideas will be presented within the context of thermoelasticity theory, without heat conduction. The hyperbolic character of the field equations causes the breakdown of smooth solutions and the development of shock waves so the class of smooth functions is far too narrow to encompass all processes of physical interest. The natural framework is the class of proper processes, characterized by the property that velocity, deformation gradient, specific entropy, stress, temperature and internal energy are functions of bounded variation.