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Information Thermodynamics of Turing Patterns.

Gianmaria Falasco1, Riccardo Rao1, Massimiliano Esposito1

  • 1Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg.

Physical Review Letters
|September 22, 2018
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Summary
This summary is machine-generated.

This study introduces a thermodynamic framework for reaction-diffusion systems far from equilibrium. It demonstrates how nonequilibrium free energy acts as a Lyapunov function and quantifies the work needed for concentration changes, revealing a thermodynamic phase transition in Turing patterns.

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Area of Science:

  • Thermodynamics
  • Chemical Kinetics
  • Non-equilibrium Systems

Background:

  • Reaction-diffusion systems are fundamental to pattern formation.
  • Understanding systems far from equilibrium requires advanced thermodynamic descriptions.
  • Chemostats control system composition, driving them out of equilibrium.

Purpose of the Study:

  • Develop a rigorous thermodynamic framework for reaction-diffusion systems under non-equilibrium conditions.
  • Construct non-equilibrium thermodynamic potentials using chemical network symmetries.
  • Analyze the role of free energy as a Lyapunov function and its relation to work.

Main Methods:

  • Assumption of local equilibrium.
  • Construction of non-equilibrium thermodynamic potentials.
  • Exploitation of chemical network topology symmetries.
  • Analysis of relaxation to equilibrium in closed and open systems.
  • Application to the one-dimensional Brusselator model.

Main Results:

  • Non-equilibrium free energy serves as a Lyapunov function for system relaxation.
  • The variation in free energy quantifies the minimum work for concentration manipulation.
  • Turing pattern formation in the Brusselator model is analytically studied.
  • Turing patterns are classified as a thermodynamic non-equilibrium phase transition.

Conclusions:

  • The developed thermodynamic framework provides a robust tool for studying complex reaction-diffusion systems.
  • The findings offer new insights into phase transitions in non-equilibrium chemical systems.
  • This work bridges statistical mechanics and chemical kinetics for non-equilibrium phenomena.