Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics
The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1330 |
| _version_ | 1797547143721910272 |
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| author | Rodrigo Cofré Cesar Maldonado Bruno Cessac |
| author_facet | Rodrigo Cofré Cesar Maldonado Bruno Cessac |
| author_sort | Rodrigo Cofré |
| collection | DOAJ |
| description | The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, in order to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism. |
| first_indexed | 2024-03-10T14:39:01Z |
| format | Article |
| id | doaj.art-87ddf52e9a104e8ea4c4fb4a2ed2423e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T14:39:01Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-87ddf52e9a104e8ea4c4fb4a2ed2423e2023-11-20T21:55:56ZengMDPI AGEntropy1099-43002020-11-012211133010.3390/e22111330Thermodynamic Formalism in Neuronal Dynamics and Spike Train StatisticsRodrigo Cofré0Cesar Maldonado1Bruno Cessac2CIMFAV-Ingemat, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso 2340000, ChileIPICYT/División de Matemáticas Aplicadas, San Luis Potosí 78216, MexicoInria Biovision team and Neuromod Institute, Université Côte d’Azur, 06901 CEDEX Inria, FranceThe Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, in order to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.https://www.mdpi.com/1099-4300/22/11/1330Thermodynamic Formalismneuronal networks dynamicsmaximum entropy principlefree energy and pressurelinear responselarge deviations |
| spellingShingle | Rodrigo Cofré Cesar Maldonado Bruno Cessac Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics Entropy Thermodynamic Formalism neuronal networks dynamics maximum entropy principle free energy and pressure linear response large deviations |
| title | Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics |
| title_full | Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics |
| title_fullStr | Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics |
| title_full_unstemmed | Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics |
| title_short | Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics |
| title_sort | thermodynamic formalism in neuronal dynamics and spike train statistics |
| topic | Thermodynamic Formalism neuronal networks dynamics maximum entropy principle free energy and pressure linear response large deviations |
| url | https://www.mdpi.com/1099-4300/22/11/1330 |
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