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Main Authors:	Teles, Tarcísio Nunes, Pakter, Renato, Levin, Yan
Format:	Preprint
Published:	2025
Subjects:	Statistical Mechanics
Online Access:	https://arxiv.org/abs/2501.15593
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author	Teles, Tarcísio Nunes Pakter, Renato Levin, Yan
author_facet	Teles, Tarcísio Nunes Pakter, Renato Levin, Yan
contents	We present a theory of collisionless relaxation in systems with long-range interactions. Contrary to Lynden-Bell's theory of violent relaxation, which assumes global ergodicity and mixing, we show that quasi-stationary states (qSS) observed in these systems exhibit broken global ergodicity. We propose that relaxation towards equilibrium occurs through a process of local mixing, where particles spread over energy shells defined by the manifold to which their trajectories are confined. To demonstrate our theory, we study the Hamiltonian Mean Field (HMF) model, a paradigmatic system with long-range interactions. Our theory accurately predicts the particle distribution functions in qSS observed in molecular dynamics simulations without any adjustable parameters. Additionally, it precisely forecasts the phase transitions observed in the HMF model.
format	Preprint
id	arxiv_https___arxiv_org_abs_2501_15593
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Mixing and Ergodicity in Systems with Long-Range Interactions Teles, Tarcísio Nunes Pakter, Renato Levin, Yan Statistical Mechanics We present a theory of collisionless relaxation in systems with long-range interactions. Contrary to Lynden-Bell's theory of violent relaxation, which assumes global ergodicity and mixing, we show that quasi-stationary states (qSS) observed in these systems exhibit broken global ergodicity. We propose that relaxation towards equilibrium occurs through a process of local mixing, where particles spread over energy shells defined by the manifold to which their trajectories are confined. To demonstrate our theory, we study the Hamiltonian Mean Field (HMF) model, a paradigmatic system with long-range interactions. Our theory accurately predicts the particle distribution functions in qSS observed in molecular dynamics simulations without any adjustable parameters. Additionally, it precisely forecasts the phase transitions observed in the HMF model.
title	Mixing and Ergodicity in Systems with Long-Range Interactions
topic	Statistical Mechanics
url	https://arxiv.org/abs/2501.15593

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