New formulation of local-equilibrium thermodynamics

Abstract

This study points out that the conventional separation of balance equations for energy in fluids into a flow and a source term is not thermodynamically valid. It corrects this inadequacy and thereby identifies an expression for the nonnegative rate of entropy production that is a sum of products of kinetic and thermodynamic quantities. Here, the kinetic and corresponding thermodynamic quantities are the flow of internal energy and the gradient of the reciprocal temperature; the flow of each component and the negative gradient of its chemical potential divided by the temperature; the rate of each chemical reaction and its affinity divided by the temperature; and the conversion of mechanical energy into internal energy and the reciprocal temperature. One of the deductions from this expression is that the internal energy of a fluid never turns into its mechanical energy on its own, a fact which had heretofore not been actually proved in general. On the other hand, the stability condition of local equilibrium leads to a nonpositive integral over the volume of a system under suitable boundary conditions. The integrand is found to be the same form as the entropy production expression, with each thermodynamic quantity replaced by its time derivative. It thus turns out that the thermodynamic quantities always vary temporally so as to lower the entropy production of the system. It can also be seen that if a particular kinetic and thermodynamic quantity pair alone is considered only locally, then the absolute value of the latter invariably lessens with time.