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Entropy 2017, 19(12), 693; https://doi.org/10.3390/e19120693

Stochastic Thermodynamics: A Dynamical Systems Approach

School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, USA
These authors contributed equally to this work.
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Received: 16 October 2017 / Revised: 13 December 2017 / Accepted: 13 December 2017 / Published: 17 December 2017
(This article belongs to the Special Issue Entropy and Its Applications across Disciplines)
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Abstract

In this paper, we develop an energy-based, large-scale dynamical system model driven by Markov diffusion processes to present a unified framework for statistical thermodynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic state space formulation, we develop a nonlinear stochastic compartmental dynamical system model characterized by energy conservation laws that is consistent with statistical thermodynamic principles. In particular, we show that the difference between the average supplied system energy and the average stored system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration. In addition, we show that the average stored system energy is equal to the mean energy that can be extracted from the system and the mean energy that can be delivered to the system in order to transfer it from a zero energy level to an arbitrary nonempty subset in the state space over a finite stopping time. View Full-Text
Keywords: statistical thermodynamics; dynamical thermodynamics; entropy; stochastic dynamical systems theory; stochastic semistability; energy equipartition; Markov processes statistical thermodynamics; dynamical thermodynamics; entropy; stochastic dynamical systems theory; stochastic semistability; energy equipartition; Markov processes
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Rajpurohit, T.; Haddad, W.M. Stochastic Thermodynamics: A Dynamical Systems Approach. Entropy 2017, 19, 693.

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