Statistical-mechanical formulation of Lyapunov exponents
Sorin Tanase-Nicola, Jorge Kurchan
TL;DR
This paper presents a novel approach to calculating Lyapunov exponents by formulating them as a problem in statistical mechanics using quantum many-body theory, enabling new analytical techniques.
Contribution
It introduces a statistical-mechanical formulation of Lyapunov exponents, linking dynamical systems to quantum many-body problems for the first time.
Findings
Lyapunov exponents can be expressed via free energy of a quantum system.
The approach allows the use of statistical mechanics techniques in dynamical systems analysis.
Provides a new perspective for studying chaos through quantum statistical models.
Abstract
We show how the Lyapunov exponents of a dynamic system can in general be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Statistical Mechanics and Entropy · Advanced Thermodynamics and Statistical Mechanics