Entropy of glass, spatial energy fluctuations and the Kauzmann paradox

Abstract

Non-zero energy fluctuations, 〈(ΔE)2〉, in a macroscopic system are characteristic of amorphous material, and lead to a non-zero entropy S=S(E). The energy fluctuations arising from spatially disordered atomic configurations contribute a structural heat capacity which, once the glass structure is frozen-in, cannot be probed by energy exchange with a heat bath. Hence calorimetry leads to erroneous estimates of extrapolated heat capacities of supercooled liquids, and to the unacceptable conjecture about existence of an `ideal glass' state of zero entropy below the glass transition. Structural entropy can be evaluated from structure data and pair potentials by modeling the radial distribution function in a functional form, g(r)=g(r;L,D), where L is an optimal virtual lattice related to the local configurations of atoms and D is a `structural diffusion' parameter specifying the degree of spatial decay of coherence between local structures in the glass. In the parameter space, {L,D}, there exists a virtual path connecting the state of glass to the virtual lattice state, L, which enables evaluation of S=S(E) by following the energy E and the spatial energy fluctuations 〈(ΔE)2〉 along the path and integrating ∂2S/∂E2=−〈(ΔE)2〉−1 from the glass state to the zero entropy state S(E0)≡S(L)=0.