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We use rigorous nonequilibrium thermodynamic arguments to establish that (i)the nonequilibrium entropy S(T_{0}) of any system is bounded below by theexperimentally (calorimetrically) determined entropy S_{expt}(T_{0}), (ii)S_{expt}(T_{0}) is bounded below by the equilibrium or stationary state (suchas 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 residualentropy S_{R} is bounded below by the extrapolated S_{expt}(0)>S_{SCL}(0) atabsolute zero. These results are very general and applicable to allnonequilibrium systems regardless of how far they are from their stationarystates.

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