Abstract
Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the literature of non-equilibrium statistical mechanics. This tutorial provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics.
Highlights
Being the brain one of the most complex systems within the observable universe, it is not surprising that there is still a large number of unanswered questions related to its structure and functions
As a prominent example of this, computational neuroscience has been greatly enriched during the last decades by tools, ideas and methods coming from statistical physics [1,2]
It is to be noted that the definition used in this tutorial for the free energy (11) follows from the conventions used in the field of thermodynamic formalism [41,45,46] and changes its sign with the usual convention in the field of statistical mechanics
Summary
Being the brain one of the most complex systems within the observable universe, it is not surprising that there is still a large number of unanswered questions related to its structure and functions. Despite the potential of interdisciplinary pollination related to these fascinating issues, many scientists find it hard to explore these topics because of the major entry barriers, including differences in jargon, conventions, and notations across the various fields To bridge this gap, this tutorial intends to provide an accessible introduction to the non-equilibrium properties of maximum entropy Markov chains, with an emphasis in spike train statistics. While not introducing novel material, the main added value of this tutorial is to present results of the field of non-equilibrium statistical mechanics in a pedagogical manner based on examples These results have direct application to maximum entropy. May shed new light on the study of spike train statistics This tutorial is suitable for researchers in the fields of physics or mathematics who are curious about the interesting questions and possibilities that computational neurosciences offers.
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