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

TL;DR

This paper uses rigorous thermodynamic arguments to establish bounds on nonequilibrium, experimental, and residual entropies, showing that residual entropy cannot be less than the extrapolated experimental entropy at absolute zero.

Contribution

It provides a general theoretical framework linking nonequilibrium, experimental, and equilibrium entropies, establishing bounds and implications for residual entropy.

Findings

Nonequilibrium entropy is bounded below by experimental entropy.

Experimental entropy is bounded below by supercooled liquid entropy.

Residual entropy at zero temperature is bounded below by extrapolated experimental entropy.

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.