The equation which governs irreversibility in continuum mechanics

Abstract

By consistently applying the concepts of Classical Thermodynamics, a general entropy equation is derived which applies to every continuous system both in equilibrium and in non-equilibrium conditions. The established equation reduces to the classical entropy equation when equilibrium conditions are considered. Outside thermodynamic equilibrium, however, it generalizes the classical equation and affords a precise relation to measure the time-rate of entropy. Being independent of the other field equations currently introduced in the theory, the present equation enables to determine the production of non-thermal energy that in non-equilibrium conditions can result from the transformation of part of the heat that flows from the hotter to the colder parts of the system. Such a production of non-thermal energy is ignored by the current theories, since they lack the appropriate equation to determine it.