期刊
ENTROPY
卷 18, 期 4, 页码 -出版社
MDPI
DOI: 10.3390/e18040140
关键词
Markov processes; biology; non-equilibrium steady states; entropy; category theory
资金
- NSF's East Asia and Pacific Summer Institutes Program (EAPSI)
- National Research Foundation of Singapore (NRF)
- NIMBIOS
- Div Of Biological Infrastructure
- Direct For Biological Sciences [1300426] Funding Source: National Science Foundation
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.
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