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Entropy 2015, 17(2), 710-754; doi:10.3390/e17020710

On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

1
Department of Physics, The University of Akron, Akron, OH 44325, USA
2
Department of Polymer Science, The University of Akron, Akron, OH 44325, USA 
Received: 2 December 2013 / Revised: 2 December 2013 / Accepted: 27 January 2015 / Published: 5 February 2015
(This article belongs to the Special Issue Advances in Methods and Foundations of Non-Equilibrium Thermodynamics)
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Abstract

We review the concept of nonequilibrium thermodynamic entropy and observables and internal variables as state variables, introduced recently by us, and provide a simple first principle derivation of additive statistical entropy, applicable to all nonequilibrium states by treating thermodynamics as an experimental science. We establish their numerical equivalence in several cases, which includes the most important case when the thermodynamic entropy is a state function. We discuss various interesting aspects of the two entropies and show that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space. We show that negative thermodynamic entropy can appear from nonnegative statistical entropy. View Full-Text
Keywords: Thermodynamic entropy; statistical entropy; second law of thermodynamics; reversible and irreversuible processes; macro- and micro-states; internal variables; state; state variables; state function; internal equilibrium; homogeneous and inhomogeneous states; temporal and ensemble averages; phase space confinement; vitrification and residual entropy; Gibbs and Boltzmann formulations; negative entropy Thermodynamic entropy; statistical entropy; second law of thermodynamics; reversible and irreversuible processes; macro- and micro-states; internal variables; state; state variables; state function; internal equilibrium; homogeneous and inhomogeneous states; temporal and ensemble averages; phase space confinement; vitrification and residual entropy; Gibbs and Boltzmann formulations; negative entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gujrati, P.D. On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies. Entropy 2015, 17, 710-754.

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