Entropic Dynamics on Gibbs Statistical Manifolds
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the sta...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/5/494 |
| _version_ | 1797536944055386112 |
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| author | Pedro Pessoa Felipe Xavier Costa Ariel Caticha |
| author_facet | Pedro Pessoa Felipe Xavier Costa Ariel Caticha |
| author_sort | Pedro Pessoa |
| collection | DOAJ |
| description | Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold that is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an “entropic” notion of time that is tailored to the system under study; the system is its own clock. As one might expect that entropic time is intrinsically directional; there is a natural arrow of time that is led by entropic considerations. As illustrative examples, we discuss dynamics on a space of Gaussians and the discrete three-state system. |
| first_indexed | 2024-03-10T12:08:02Z |
| format | Article |
| id | doaj.art-d35043cc767d4fe0bc90eafeaaab6ba8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T12:08:02Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d35043cc767d4fe0bc90eafeaaab6ba82023-11-21T16:27:09ZengMDPI AGEntropy1099-43002021-04-0123549410.3390/e23050494Entropic Dynamics on Gibbs Statistical ManifoldsPedro Pessoa0Felipe Xavier Costa1Ariel Caticha2Department of Physics, University at Albany (SUNY), Albany, NY 12222, USADepartment of Physics, University at Albany (SUNY), Albany, NY 12222, USADepartment of Physics, University at Albany (SUNY), Albany, NY 12222, USAEntropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold that is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an “entropic” notion of time that is tailored to the system under study; the system is its own clock. As one might expect that entropic time is intrinsically directional; there is a natural arrow of time that is led by entropic considerations. As illustrative examples, we discuss dynamics on a space of Gaussians and the discrete three-state system.https://www.mdpi.com/1099-4300/23/5/494entropic dynamicsmaximum entropyinformation geometrycanonical distributionsexponential family |
| spellingShingle | Pedro Pessoa Felipe Xavier Costa Ariel Caticha Entropic Dynamics on Gibbs Statistical Manifolds Entropy entropic dynamics maximum entropy information geometry canonical distributions exponential family |
| title | Entropic Dynamics on Gibbs Statistical Manifolds |
| title_full | Entropic Dynamics on Gibbs Statistical Manifolds |
| title_fullStr | Entropic Dynamics on Gibbs Statistical Manifolds |
| title_full_unstemmed | Entropic Dynamics on Gibbs Statistical Manifolds |
| title_short | Entropic Dynamics on Gibbs Statistical Manifolds |
| title_sort | entropic dynamics on gibbs statistical manifolds |
| topic | entropic dynamics maximum entropy information geometry canonical distributions exponential family |
| url | https://www.mdpi.com/1099-4300/23/5/494 |
| work_keys_str_mv | AT pedropessoa entropicdynamicsongibbsstatisticalmanifolds AT felipexaviercosta entropicdynamicsongibbsstatisticalmanifolds AT arielcaticha entropicdynamicsongibbsstatisticalmanifolds |