Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality
Abstract
In this paper we revisit the notion of the “minus logarithm of stationary probability” as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that this quantity arises naturally through both monotonicity results of Markov processes and as the rate function when a stochastic process approaches a detrministic limit. We then undertake a more detailed mathematical analysis of the consequences of this quantity, culminating in a necessary and sufficient condition for the criticality of stochastic systems. This condition is then discussed in the context of recent results about criticality in biological systems.
 Authors:
 Publication Date:
 Research Org.:
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1340861
 Report Number(s):
 PNNLSA119608
Journal ID: ISSN 10994300
 DOE Contract Number:
 AC0576RL01830
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Entropy; Journal Volume: 18; Journal Issue: 8
 Country of Publication:
 United States
 Language:
 English
 Subject:
 nonequilibium steady states; stochastic nonequilibrium thermodynamics; generalized potentials; entropy
Citation Formats
Thompson, Lowell, and Qian, Hong. Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality. United States: N. p., 2016.
Web. doi:10.3390/e18080309.
Thompson, Lowell, & Qian, Hong. Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality. United States. doi:10.3390/e18080309.
Thompson, Lowell, and Qian, Hong. 2016.
"Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality". United States.
doi:10.3390/e18080309.
@article{osti_1340861,
title = {Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality},
author = {Thompson, Lowell and Qian, Hong},
abstractNote = {In this paper we revisit the notion of the “minus logarithm of stationary probability” as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that this quantity arises naturally through both monotonicity results of Markov processes and as the rate function when a stochastic process approaches a detrministic limit. We then undertake a more detailed mathematical analysis of the consequences of this quantity, culminating in a necessary and sufficient condition for the criticality of stochastic systems. This condition is then discussed in the context of recent results about criticality in biological systems.},
doi = {10.3390/e18080309},
journal = {Entropy},
number = 8,
volume = 18,
place = {United States},
year = 2016,
month = 8
}

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