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

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

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Received: 13 January 2010; in revised form: 9 June 2010 / Accepted: 21 June 2010 / Published: 24 June 2010
(This article belongs to the Special Issue Entropy, Order and Symmetry)
Download PDF [596 KB, uploaded 24 June 2010]
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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Gujrati PD. Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics. Symmetry. 2010; 2(3):1201-1249.

Chicago/Turabian Style

Gujrati, Purushottam D. 2010. "Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics." Symmetry 2, no. 3: 1201-1249.


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