Non-equilibrium Onsager-Machlup theory
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910642225545216 |
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| author | Peredo-Ortiz, Ricardo Elizondo-Aguilera, Luis F. Ramírez-González, Pedro E. Lázaro-Lázaro, Edilio Mendoza-Méndez, Patricia Medina-Noyola, Magdaleno |
| author_facet | Peredo-Ortiz, Ricardo Elizondo-Aguilera, Luis F. Ramírez-González, Pedro E. Lázaro-Lázaro, Edilio Mendoza-Méndez, Patricia Medina-Noyola, Magdaleno |
| contents | This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or \emph{"piecewise"}) stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein-Uhlenbeck stochastic process (which is \emph{globally} stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager-Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear, and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager-Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the \emph{non-equilibrium self-consistent generalized Langevin equation} (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and the gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-equilibrium Onsager-Machlup theory Peredo-Ortiz, Ricardo Elizondo-Aguilera, Luis F. Ramírez-González, Pedro E. Lázaro-Lázaro, Edilio Mendoza-Méndez, Patricia Medina-Noyola, Magdaleno Statistical Mechanics Mathematical Physics This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or \emph{"piecewise"}) stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein-Uhlenbeck stochastic process (which is \emph{globally} stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager-Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear, and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager-Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the \emph{non-equilibrium self-consistent generalized Langevin equation} (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and the gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model. |
| title | Non-equilibrium Onsager-Machlup theory |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2311.00120 |