Non-equilibrium thermodynamics.III. Thermodynamic Principles, Entropy Continuity during Component Confinement, Energy Gap and the Residual Entropy

TL;DR

This paper explores the thermodynamic principles governing non-equilibrium systems during component confinement, demonstrating the continuity of entropy and Gibbs free energy, and justifying the existence of residual entropy in glasses.

Contribution

It establishes the continuity of entropy and Gibbs free energy during glass transition and formulates thermodynamic principles applicable to non-equilibrium systems.

Findings

Entropy remains continuous during component confinement.

Residual entropy in glasses is justified by thermodynamic principles.

The second law supports the non-zero residual entropy at absolute zero.

Abstract

To investigate the consequences of component confinement such as at a glass transition and the well-known energy or enthalpy gap (between the glass and the perfect crystal at absolute zero, see text), we follow our previous approach [Phys. Rev. E 81, 051130 (2010)] of using the second law applied to an isolated system {\Sigma}_0 consisting of the homogeneous system {\Sigma} and the medium {\Sigma}. We establish on general grounds the continuity of the Gibbs free energy G(t) of {\Sigma} as a function of time at fixed temperature and pressure of the medium. It immediately follows from this and the observed continuity of the enthalpy during component confinement that the entropy S of the open system {\Sigma} must remain continuous during a component confinement such as at a glass transition. We use these continuity properties and the recently developed non-equilibrium thermodynamics to formulate thermodynamic principles of additivity, reproducibility, continuity and stability that must also apply to non-equilibrium systems in internal equilibrium. We find that the irreversibility during a glass transition only justifies the residual entropy S_{R} to be at least as much as that determined by disregarding the irreversibility, a common practice in the field. This justifies a non-zero residual entropy S_{R} in glasses, which is also in accordance with the energy or enthalpy gap at absolute zero. We develop a statistical formulation of the entropy of a non-equilibrium system, which results in the continuity of entropy during component confinement in accordance with the second law and sheds light on the mystery behind the residual entropy, which is consistent with the recent conclusion [Symmetry 2, 1201 (2010)] drawn by us.