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Entropy 2016, 18(4), 140; doi:10.3390/e18040140

Open Markov Processes: A Compositional Perspective on Non-Equilibrium Steady States in Biology

Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
Academic Editors: John Baez, John Harte, Marc Harper and Kevin H. Knuth
Received: 5 January 2016 / Revised: 16 February 2016 / Accepted: 6 April 2016 / Published: 15 April 2016
(This article belongs to the Special Issue Information and Entropy in Biological Systems)
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Abstract

In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These “open Markov processes” serve as the building blocks for more complicated processes. In this paper, we describe the potential application of this framework in the modeling of biological systems as open systems maintained away from equilibrium. We show that non-equilibrium steady states emerge in open systems of this type, even when the rates of the underlying process are such that a detailed balanced equilibrium is permitted. It is shown that these non-equilibrium steady states minimize a quadratic form which we call “dissipation”. In some circumstances, the dissipation is approximately equal to the rate of change of relative entropy plus a correction term. On the other hand, Prigogine’s principle of minimum entropy production generally fails for non-equilibrium steady states. We use a simple model of membrane transport to illustrate these concepts. View Full-Text
Keywords: Markov processes; biology; non-equilibrium steady states; entropy; category theory Markov processes; biology; non-equilibrium steady states; entropy; category theory
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. (CC BY 4.0).

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Pollard, B.S. Open Markov Processes: A Compositional Perspective on Non-Equilibrium Steady States in Biology. Entropy 2016, 18, 140.

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