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The Maximum Caliber Variational Principle for Nonequilibria.

Kingshuk Ghosh1, Purushottam D Dixit2,3, Luca Agozzino4

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Maximum caliber, a principle like maximum entropy, predicts material equilibria and nonequilibrium flows. It offers new insights into complex systems, from gene circuits to neuronal firing.

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Area of Science:

  • Statistical mechanics
  • Complex systems theory
  • Non-equilibrium thermodynamics

Background:

  • Classical thermodynamics relies on entropy maximization for equilibrium predictions.
  • A general variational principle for non-equilibrium systems has been lacking.
  • E.T. Jaynes, Shore, and Johnson introduced new avenues in 1980.

Purpose of the Study:

  • To review the principle of maximum caliber.
  • To highlight its application in inferring distributions of flows over pathways.
  • To demonstrate its utility in understanding complex systems.

Main Methods:

  • Review of maximum caliber principle.
  • Application to inferring flow distributions under dynamical constraints.
  • Analysis of complex systems using this principle.

Main Results:

  • Maximum caliber provides a framework for non-equilibrium situations.
  • It successfully infers distributions of flows over pathways.
  • New insights are gained into various complex systems.

Conclusions:

  • Maximum caliber is a powerful tool for non-equilibrium statistical mechanics.
  • It offers a complementary approach to maximum entropy.
  • Its applications span diverse fields including biology, physics, and computer science.