The role of stress in mass transport

The fundamental criteria of thermodynamic equilibrium and stabihty are usually stated in somewhat different terms, but the equivalence to the fundamental criteria is readily established for the physical systems of interest here. The first law of thermodynamics states that the rate of change of internal energy U of a material system equals the rate at which work W is being done on it plus the rate at which heat Q is being added to it, or 

In general, work and heat can be a added through boundaries or through volumetric influences body forces, radiation absorption, and so on. In addition, work can be dissipated internally as heat through deformation for some materials. The entropy T L of the system is the portion of the internal energy that cannot be recovered as work and that exists as heat 

An immediate consequence is that the closed system will be in stable equilibrium if and only if the entropy of that system is maximum under all admissible variations of its configuration. The stability can be local or global, depending on whether the variations of state used to probe stability are infinitesimal or arbitrary in magnitude. This is the form of the original statement on equilibrium and stability of material systems Gibbs (1876).  

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