Some Rigorous Results Relating Nonequilibrium, Equilibrium, Calorimetrically Measured and Residual Entropies during Cooling

Abstract

We use rigorous nonequilibrium thermodynamic arguments to establish that (i) the nonequilibrium entropy S(T_{0}) of any system is bounded below by the experimentally (calorimetrically) determined entropy S_{expt}(T_{0}), (ii) S_{expt}(T_{0}) is bounded below by the equilibrium or stationary state (such as the supercooled liquid) entropy S_{SCL}(T_{0}) and consequently (iii) S(T_{0}) cannot drop below S_{SCL}(T_{0}). It then follows that the residual entropy S_{R} is bounded below by the extrapolated S_{expt}(0)>S_{SCL}(0) at absolute zero. These results are very general and applicable to all nonequilibrium systems regardless of how far they are from their stationary states.