Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-equilibrium thermodynamics.III. Thermodynamic Principles, Entropy
  Continuity during Component Confinement, Energy Gap and the Residual Entropy   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.

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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: eess