| Autor: |
Nahuel Freitas, Gianmaria Falasco, Massimiliano Esposito |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
New Journal of Physics, Vol 23, Iss 9, p 093003 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
1367-2630 |
| DOI: |
10.1088/1367-2630/ac1bf5 |
| Popis: |
We consider thermodynamically consistent autonomous Markov jump processes displaying a macroscopic limit in which the logarithm of the probability distribution is proportional to a scale-independent rate function (i.e. a large deviations principle is satisfied). In order to provide an explicit expression for the probability distribution valid away from equilibrium, we propose a linear response theory performed at the level of the rate function. We show that the first order non-equilibrium contribution to the steady state rate function, g ( x ), satisfies $\boldsymbol{u}(\boldsymbol{x})\cdot \nabla g(\boldsymbol{x})=-\beta \dot {W}(\boldsymbol{x})$ where the vector field u ( x ) defines the macroscopic deterministic dynamics, and the scalar field $\dot {W}(\boldsymbol{x})$ equals the rate at which work is performed on the system in a given state x . This equation provides a practical way to determine g ( x ), significantly outperforms standard linear response theory applied at the level of the probability distribution, and approximates the rate function surprisingly well in some far-from-equilibrium conditions. The method applies to a wealth of physical and chemical systems, that we exemplify by two analytically tractable models—an electrical circuit and an autocatalytic chemical reaction network—both undergoing a non-equilibrium transition from a monostable phase to a bistable phase. Our approach can be easily generalized to transient probabilities and non-autonomous dynamics. Moreover, its recursive application generates a virtual flow in the probability space which allows to determine the steady state rate function arbitrarily far from equilibrium. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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