Hamilton's Principle and Nonequilibrium Thermodynamics

Abstract

A variational principle, analogous to Hamilton's principle of mechanics, is proposed which leads to the equations of both nonequilibrium thermodynamics and hydrodynamics. The Onsager relations are equivalent to the use of a heat production function ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{u}}_{d}$, analogous to the Rayleigh dissipation function. ${\mathrm{du}}_{c}$, where ${\mathrm{du}}_{c}=du\ensuremath{-}{\mathrm{du}}_{d}$, is used as the total differential of the potential energy. $\mathrm{du}$ represents the total change in the internal energy. Limitations of the theory are briefly considered. The effect of an applied magnetic field is briefly considered in an Appendix. The Onsager relations are derived for a system held in a magnetic field.