Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

TL;DR

This paper reviews how Thermodynamic Formalism offers a rigorous mathematical framework to analyze neuronal dynamics and spike train statistics, linking complex system behavior with statistical inference in neuroscience.

Contribution

It introduces the application of Thermodynamic Formalism as a conceptual and operational tool in theoretical neuroscience for analyzing neuron interactions and spike data.

Findings

Provides a conceptual link between neuron dynamics and spike statistics.

Highlights open problems and future perspectives in applying formalism to neuroscience.

Reviews the use of Gibbs measures in modeling neural systems.

Abstract

The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle corresponding, 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, 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.