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Thermodynamics of chaotic relaxation processes
1School of Mathematical Sciences, <a href="https://ror.org/03jc41j30">Jiangsu University</a>, Zhenjiang 212013, China.
Physical Review. E
|September 19, 2024
Summary
This study extends thermodynamic formalism to non-equilibrium chaotic systems, linking information and escape rates to observable averages. The new theory predicts phase-space profiles of observables using transfer operator eigenfunctions.
Area of Science:
- Thermodynamics
- Non-equilibrium statistical mechanics
- Chaos theory
Background:
- Established thermodynamic formalism applies to systems at statistical equilibrium.
- Many complex systems exist in non-equilibrium states before reaching steady states.
Purpose of the Study:
- Generalize thermodynamic formalism to non-equilibrium systems out of steady state.
- Establish a finite-time relationship between information, escape rate, and observable averages.
- Develop a method to predict phase-space profiles of observables.
Main Methods:
- Generalization of thermodynamic formalism for chaotic dynamics.
- Derivation of a relation between information, escape rate, and phase-space averages.
- Utilizing leading and subleading eigenfunctions of Perron-Frobenius or Koopman transfer operators.
Main Results:
- A generalized thermodynamic formalism for finite-time dynamics of non-equilibrium chaotic systems.
- A predictive framework for the phase-space profile of integrated observables.
- Analytical and numerical validation on benchmark chaotic maps (Bernoulli, perturbed cat, Hénon, Ikeda).
Conclusions:
- The developed theory accurately describes non-equilibrium chaotic dynamics.
- Transfer operator eigenfunctions provide key insights into observable distributions.
- The approach offers a powerful tool for analyzing complex systems beyond equilibrium.
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