Why does entropy drive evolution equations?
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918378969497600 |
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| author | Peletier, Mark A. |
| author_facet | Peletier, Mark A. |
| contents | `Entropy' appears as driving force in many different evolution equations, both deterministic and stochastic, and in these equations this `entropy' also takes different forms. We show how all these examples can be understood as different instances of a common principle: Entropy drives evolutions because it characterizes the invariant measure of an underlying stochastic process. This interpretation explains the appearance of entropy, the different forms that entropy takes in these equations, and how entropy `drives' these evolution equations. We illustrate this common structure with examples from stochastic processes, gradient flows, and GENERIC systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07653 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Why does entropy drive evolution equations? Peletier, Mark A. Dynamical Systems Mathematical Physics Analysis of PDEs Functional Analysis Probability 35Q84, 37L05, 60F10, 60H10, 60K35, 82C31, 70H99 `Entropy' appears as driving force in many different evolution equations, both deterministic and stochastic, and in these equations this `entropy' also takes different forms. We show how all these examples can be understood as different instances of a common principle: Entropy drives evolutions because it characterizes the invariant measure of an underlying stochastic process. This interpretation explains the appearance of entropy, the different forms that entropy takes in these equations, and how entropy `drives' these evolution equations. We illustrate this common structure with examples from stochastic processes, gradient flows, and GENERIC systems. |
| title | Why does entropy drive evolution equations? |
| topic | Dynamical Systems Mathematical Physics Analysis of PDEs Functional Analysis Probability 35Q84, 37L05, 60F10, 60H10, 60K35, 82C31, 70H99 |
| url | https://arxiv.org/abs/2603.07653 |