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

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We use rigorous nonequilibrium thermodynamic arguments to establish that (i) the nonequilibrium entropy S(T₀) of any system is bounded below by the experimentally (calorimetrically) determined entropy Sexpt(T₀), (ii) Sexpt(T₀) is bounded below by the equilibrium or stationary state (such as the supercooled liquid) entropy SSCL(T₀) and consequently (iii) S(T₀) cannot drop below SSCL(T₀). It then follows that the residual entropy Sᵣ is bounded below by the extrapolated Sexpt(0)>SSCL(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.