PMID: 22587082May 17, 2012Paper

Shannon-entropy-based nonequilibrium "entropic" temperature of a general distribution

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
K R Narayanan, A R Srinivasa

Abstract

The concept of temperature is one of the key ideas in describing the thermodynamical properties of systems. In classical statistical mechanics of ideal gases, the notion of temperature can be described in at least two different ways: the kinetic temperature (related to the average kinetic energy of the particles) and the thermodynamic temperature (related to the ratio between infinitesimal changes in entropy and energy). For the Boltzmann distribution, the two notions lead to the same result. However, for nonequilibrium phenomena, while the kinetic temperature has been commonly used both for theoretical and simulation purposes, there appears to be no corresponding general definition of thermodynamic or entropic temperature. In this paper, we consider the statistical or Shannon entropy of a system and use the "de Bruijn identity" from information theory (see Appendix A 2 for a derivation of this identity) to show that it is possible to define a "Shannon temperature" or "entropic temperature" T for a nonequilibrium system as the ratio between the average curvature of the Hamiltonian function associated with the system and the trace of the Fisher information matrix of the nonequilibrium probability distribution (see Appendix A 1 f...Continue Reading

References

Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Takahiro Hatano, David Jou
Jul 21, 2006·The Journal of Physical Chemistry. B·D RegueraJ M G Vilar
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Eric BertinMichel Droz
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Wm G Hoover, Carol G Hoover
Aug 7, 2008·The Journal of Chemical Physics·J-L GardenH Guillou

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Citations

Mar 24, 2016·The Journal of Chemical Physics·Jacob LykkeboGemma C Solomon
Apr 20, 2019·Physical Review. E·Leonardo Ferreira Calazans, Ronald Dickman
Oct 15, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Somrita Ray, Bidhan Chandra Bag
Apr 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Somrita RayBidhan Chandra Bag

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