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Symmetry 2010, 2(3), 1201-1249; doi:10.3390/sym2031201

Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics

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: 13 January 2010 / Revised: 9 June 2010 / Accepted: 21 June 2010 / Published: 24 June 2010
(This article belongs to the Special Issue Entropy, Order and Symmetry)
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Abstract

A detailed analysis of deterministic (one-to-one) and stochastic (one-to-many) dynamics establishes that dS/dt > 0 is only consistent with the latter, which contains violation of temporal symmetry and homogeneity. We observe that the former only supports dS/dt = 0 and cannot give rise to Boltzmann’s molecular chaos assumption. The ensemble average is more meaningful than the temporal average, especially in non-equilibrium statistical mechanics of systems confined to disjoint phase space components, which commonly occurs at low temperatures. We propose that the stochasticity arises from extra degrees of freedom, which are not part of the system. We provide a simple resolution of the recurrence and irreversibility paradoxes.
Keywords: deterministic and stochastic dynamics; temporal asymmetry and inhomogeneity; second law of thermodynamics; temporal and ensemble averages; phase space confinement; irreversibility and recurrence paradoxes; molecular chaos assumption; Poincare recurrence deterministic and stochastic dynamics; temporal asymmetry and inhomogeneity; second law of thermodynamics; temporal and ensemble averages; phase space confinement; irreversibility and recurrence paradoxes; molecular chaos assumption; Poincare recurrence
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Gujrati, P.D. Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics. Symmetry 2010, 2, 1201-1249.

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