Abstract
This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry. First a non-equilibrium state space is introduced as the third key element besides the first and second law of thermodynamics. This state space provides the mathematical structure to generalize the Gibbs fundamental relation to non-equilibrium thermodynamics. A unique formulation for the second law of thermodynamics is postulated and it showed how the complying concept for non-equilibrium entropy is retrieved. The foundation of this formulation is a physical quantity, which is in non-equilibrium thermodynamics nowhere equal to zero. This is another perspective compared to the inequality, which is used in most other formulations in the literature. Based on this mathematical framework, it is proven that the thermodynamic potential is defined by the Gibbs free energy. The set of conjugated coordinates in the mathematical structure for the Gibbs fundamental relation will be identified for single component, closed systems. Only in the final section of this contribution will the equilibrium constraint be introduced and applied to obtain some familiar formulations for classical (equilibrium) thermodynamics.
Highlights
This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry
There are two key components in this innovative derivation: 1) a generalization of Gibbs fundamental relation for non-equilibrium thermodynamics that is based on the dissipation of energy and 2) a unique formulation of the second law of thermodynamics, including a mathematical proper derivation of non-equilibrium entropy as a thermodynamic state function
This paper presents the mathematical framework of Classical Non-Equilibrium
Summary
There are two key components in this innovative derivation: 1) a generalization of Gibbs fundamental relation for non-equilibrium thermodynamics that is based on the dissipation of energy and 2) a unique formulation of the second law of thermodynamics, including a mathematical proper derivation of non-equilibrium entropy as a thermodynamic state function. The step is to postulate a unique formulation for the second law of thermodynamics and the complying derivation of non-equilibrium entropy With this identification, a generalized Gibbs fundamental relation for non-equilibrium thermodynamics is derived, which includes sufficient additional degrees of freedom to model non-equilibrium phenomena. It will be shown how the equilibrium constraint reduces Gibbs fundamental relation to a Pfaffian equation, which is the basis for the derivation of the so-called Maxwell relations in thermodynamics [3] [5] [6] [7]
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