The Second Law of Thermodynamics and Stability,

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1978
Accession Number
ADA064091

Entities

People

  • C. M. Dafermos

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Adiabatic Processes
  • Applied Mathematics
  • Boundary Value Problems
  • Elastic Materials
  • Elastic Properties
  • Energy
  • Entropy
  • Equations
  • Equations Of State
  • Heat Energy
  • Inequalities
  • Materials
  • Mechanics
  • Shock Waves
  • Thermodynamic Processes
  • Thermodynamics
  • Two Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.
  • Thermal Physics or Thermal Science.