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Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

1
CIMFAV-Ingemat, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso 2340000, Chile
2
IPICYT/División de Matemáticas Aplicadas, San Luis Potosí 78216, Mexico
3
Inria Biovision team and Neuromod Institute, Université Côte d’Azur, 06901 CEDEX Inria, France
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(11), 1330; https://doi.org/10.3390/e22111330
Received: 9 October 2020 / Revised: 13 November 2020 / Accepted: 15 November 2020 / Published: 23 November 2020
(This article belongs to the Special Issue Generalized Statistical Thermodynamics)
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. View Full-Text
Keywords: Thermodynamic Formalism; neuronal networks dynamics; maximum entropy principle; free energy and pressure; linear response; large deviations; ergodic theory Thermodynamic Formalism; neuronal networks dynamics; maximum entropy principle; free energy and pressure; linear response; large deviations; ergodic theory
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MDPI and ACS Style

Cofré, R.; Maldonado, C.; Cessac, B. Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics. Entropy 2020, 22, 1330. https://doi.org/10.3390/e22111330

AMA Style

Cofré R, Maldonado C, Cessac B. Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics. Entropy. 2020; 22(11):1330. https://doi.org/10.3390/e22111330

Chicago/Turabian Style

Cofré, Rodrigo; Maldonado, Cesar; Cessac, Bruno. 2020. "Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics" Entropy 22, no. 11: 1330. https://doi.org/10.3390/e22111330

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