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Main Author: Lippolis, Domenico
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2402.11976
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author Lippolis, Domenico
author_facet Lippolis, Domenico
contents Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting distribution, that rules the long-time average of every observable of interest. Before that asymptotic timescale, the statistics of chaos is generally believed to depend on both the initial conditions and the chosen observable. I show that this is not the case for a widely applicable class of models, that feature a phase-space (`field') distribution common to all pushed-forward or integrated observables, while the system is still relaxing towards statistical equilibrium or a steady state. This universal profile is determined by both leading and first subleading eigenfunctions of the transport operator (Koopman or Perron-Frobenius) that maps phase-space densities forward or backward in time.
format Preprint
id arxiv_https___arxiv_org_abs_2402_11976
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Chaotic fields out of equilibrium are observable independent
Lippolis, Domenico
Chaotic Dynamics
Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting distribution, that rules the long-time average of every observable of interest. Before that asymptotic timescale, the statistics of chaos is generally believed to depend on both the initial conditions and the chosen observable. I show that this is not the case for a widely applicable class of models, that feature a phase-space (`field') distribution common to all pushed-forward or integrated observables, while the system is still relaxing towards statistical equilibrium or a steady state. This universal profile is determined by both leading and first subleading eigenfunctions of the transport operator (Koopman or Perron-Frobenius) that maps phase-space densities forward or backward in time.
title Chaotic fields out of equilibrium are observable independent
topic Chaotic Dynamics
url https://arxiv.org/abs/2402.11976