Foundations of algorithmic thermodynamics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910721229455360 |
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| author | Ebtekar, Aram Hutter, Marcus |
| author_facet | Ebtekar, Aram Hutter, Marcus |
| contents | Gács' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables or probabilistic ensembles, rendering it applicable to settings arbitrarily far from equilibrium. For measure-preserving dynamical systems equipped with a Markovian coarse-graining, we prove a number of fluctuation inequalities. These include algorithmic versions of Jarzynski's equality, Landauer's principle, and the second law of thermodynamics. In general, the algorithmic entropy determines a system's actual capacity to do work from an individual state, whereas the Gibbs-Shannon entropy only gives the mean capacity to do work from a state ensemble that is known a priori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06927 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Foundations of algorithmic thermodynamics Ebtekar, Aram Hutter, Marcus Statistical Mechanics Information Theory 68Q30 (Primary) 60J10 (Secondary) E.4; G.3; J.2 Gács' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables or probabilistic ensembles, rendering it applicable to settings arbitrarily far from equilibrium. For measure-preserving dynamical systems equipped with a Markovian coarse-graining, we prove a number of fluctuation inequalities. These include algorithmic versions of Jarzynski's equality, Landauer's principle, and the second law of thermodynamics. In general, the algorithmic entropy determines a system's actual capacity to do work from an individual state, whereas the Gibbs-Shannon entropy only gives the mean capacity to do work from a state ensemble that is known a priori. |
| title | Foundations of algorithmic thermodynamics |
| topic | Statistical Mechanics Information Theory 68Q30 (Primary) 60J10 (Secondary) E.4; G.3; J.2 |
| url | https://arxiv.org/abs/2308.06927 |