Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, what is thermodynamics, has remained unanswered. We answer this question here. Generalized statistical thermodyna...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/9/890 |
| _version_ | 1828391335812399104 |
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| author | Themis Matsoukas |
| author_facet | Themis Matsoukas |
| author_sort | Themis Matsoukas |
| collection | DOAJ |
| description | Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, what is thermodynamics, has remained unanswered. We answer this question here. Generalized statistical thermodynamics is a variational calculus of probability distributions. It is independent of physical hypotheses but provides the means to incorporate our knowledge, assumptions and physical models about a stochastic processes that gives rise to the probability in question. We derive the familiar calculus of thermodynamics via a probabilistic argument that makes no reference to physics. At the heart of the theory is a space of distributions and a special functional that assigns probabilities to this space. The maximization of this functional generates the mathematical network of thermodynamic relationship. We obtain statistical mechanics as a special case and make contact with Information Theory and Bayesian inference. |
| first_indexed | 2024-12-10T07:00:10Z |
| format | Article |
| id | doaj.art-70cff0e99e3d4b6ab9e84082f6bbdf44 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-12-10T07:00:10Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-70cff0e99e3d4b6ab9e84082f6bbdf442022-12-22T01:58:21ZengMDPI AGEntropy1099-43002019-09-0121989010.3390/e21090890e21090890Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability DistributionsThemis Matsoukas0Department of Chemical Engineering, Pennsylvania State University, University Park, PA 16802, USAStatistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, what is thermodynamics, has remained unanswered. We answer this question here. Generalized statistical thermodynamics is a variational calculus of probability distributions. It is independent of physical hypotheses but provides the means to incorporate our knowledge, assumptions and physical models about a stochastic processes that gives rise to the probability in question. We derive the familiar calculus of thermodynamics via a probabilistic argument that makes no reference to physics. At the heart of the theory is a space of distributions and a special functional that assigns probabilities to this space. The maximization of this functional generates the mathematical network of thermodynamic relationship. We obtain statistical mechanics as a special case and make contact with Information Theory and Bayesian inference.https://www.mdpi.com/1099-4300/21/9/890statistical thermodynamicsstatistical mechanicsbiased samplingmost probable distribution |
| spellingShingle | Themis Matsoukas Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions Entropy statistical thermodynamics statistical mechanics biased sampling most probable distribution |
| title | Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions |
| title_full | Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions |
| title_fullStr | Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions |
| title_full_unstemmed | Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions |
| title_short | Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions |
| title_sort | thermodynamics beyond molecules statistical thermodynamics of probability distributions |
| topic | statistical thermodynamics statistical mechanics biased sampling most probable distribution |
| url | https://www.mdpi.com/1099-4300/21/9/890 |
| work_keys_str_mv | AT themismatsoukas thermodynamicsbeyondmoleculesstatisticalthermodynamicsofprobabilitydistributions |