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Entropy Production and Irreversibility in the Linearized Stochastic Amari Neural Model.

Dario Lucente1, Giacomo Gradenigo2,3, Luca Salasnich4,5

  • 1Department of Mathematics & Physics, University of Campania "Luigi Vanvitelli", Viale Lincoln 5, 81100 Caserta, Italy.

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This study analyzes entropy production in the Amari brain model with added stochasticity. It reveals conditions for thermal equilibrium and links entropy production to Shannon entropy changes in neural networks.

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Area of Science:

  • Computational Neuroscience
  • Statistical Mechanics
  • Non-equilibrium Thermodynamics

Background:

  • The brain, as a dynamical system, operates out of thermal equilibrium.
  • Entropy production is a key observable for determining equilibrium in non-equilibrium systems.
  • The Amari model provides a coarse-grained representation of neural network dynamics.

Purpose of the Study:

  • To calculate entropy production in the stochastic Amari model.
  • To investigate the relationship between noise properties and model equilibrium.
  • To derive conditions under which the neural network model is in or out of equilibrium.

Main Methods:

  • Application of non-equilibrium statistical mechanics and stochastic processes.
  • Detailed calculation of entropy production for the Amari integro-differential equation with added noise.
  • Derivation of explicit formulae for equilibrium and non-equilibrium stationary states.

Main Results:

  • Identified specific conditions and explicit formulae for when the Amari model's stationary state is in or out of thermal equilibrium.
  • Demonstrated the interplay between noise characteristics and the model's inherent dynamics.
  • Established a relationship between the rate of entropy production and the temporal variation of the system's Shannon entropy.

Conclusions:

  • The study provides a framework for analyzing non-equilibrium dynamics in neural network models.
  • Understanding entropy production is crucial for characterizing the brain's operational state.
  • The findings offer insights into the fundamental physics governing neural computation.