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Maximum Configuration Principle for Driven Systems with Arbitrary Driving.

Rudolf Hanel1,2, Stefan Thurner1,2,3,4

  • 1Section for the Science of Complex Systems, CeMSIIS, Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria.

Entropy (Basel, Switzerland)
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Summary
This summary is machine-generated.

This study introduces a new entropy functional for driven dissipative systems, extending beyond Boltzmann-Gibbs-Shannon entropy. This framework enables a statistical theory for non-equilibrium systems with memory.

Keywords:
driven systemsmaximum configurationmaximum entropy principlenon-equilibriumstatistical mechanics

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Area of Science:

  • Statistical Mechanics
  • Non-Equilibrium Thermodynamics
  • Information Theory

Background:

  • Entropy has diverse definitions (thermodynamic, information, statistical inference).
  • Boltzmann-Gibbs-Shannon entropy (H) applies to equilibrium systems or those without memory.
  • For systems with memory (driven, self-reinforcing), distinct entropy concepts emerge, differing from H.

Purpose of the Study:

  • To develop a framework for maximum configuration entropy in driven dissipative systems.
  • To derive the entropy functional for observable state distributions in such systems.
  • To establish a statistical theory for driven non-equilibrium systems.

Main Methods:

  • Focus on maximum configuration entropy for predicting empirical distribution functions.
  • Development of a framework for driven dissipative systems.
  • Analysis using sample space reducing (SSR) processes as an analytically tractable model.

Main Results:

  • Derived a novel entropy functional for driven dissipative systems.
  • Demonstrated a consistent framework for maximum configuration entropy in non-equilibrium systems.
  • Established the technical means for a statistical theory of driven dissipative systems.

Conclusions:

  • A consistent framework for maximum configuration entropy exists for driven non-equilibrium systems.
  • This work provides the foundation for a statistical and thermodynamic theory of driven processes.
  • The Legendre structure for driven systems is discussed.