Abstract
Evolution equations are constructed that predict the particular non-equilibrium process that a body follows from a given non-equilibrium state. This construction has several advantages over classical constructions for non-equilibrium processes described in Chapter 1 Most importantly, the nonlinear evolution equations constructed satisfy the second law of thermodynamics. The non-equilibrium construction generalizes that of the Gibbs geometric surface for an equilibrium thermostatic energy density function rather than assuming a linear flux evolution equation as in Linear Irreversible Thermodynamics (LIT) or rather than assuming the Clausius-Duhem inequality as in continuum thermodynamics. No local equilibrium assumption is required. Because the construction generalizes the Gibbs construction, the non-equilibrium processes lie on a simple geometric surface that is the graph of a generalized energy density function. A more complex geometric interpretation in terms of contact structures is given in Chapter 7.
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