Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

• Main Authors: Rodrigo Cofré, Cesar Maldonado, Bruno Cessac
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Entropy
• Subjects: Thermodynamic Formalism; neuronal networks dynamics; maximum entropy principle; free energy and pressure; linear response; large deviations, ergodic theory
• Online Access: https://www.mdpi.com/1099-4300/22/11/1330

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 corresonds, 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.