Stationary states of random Hamiltonian systems

J. Fritz, Tadahisa Funaki, J. L. Lebowitz

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

We investigate the ergodic properties of Hamiltonian systems subjected to local random, energy conserving perturbations. We prove for some cases, e.g. anharmonic crystals with random nearest neighbor exchanges (or independent random reflections) of velocities, that all translation invariant stationary states with finite entropy per unit volume are microcanonical Gibbs states. The results can be utilized in proving hydrodynamic behavior of such systems.

Original languageEnglish
Pages (from-to)211-236
Number of pages26
JournalProbability Theory and Related Fields
Volume99
Issue number2
DOIs
Publication statusPublished - 1994 Jun
Externally publishedYes

Fingerprint

Random Systems
Stationary States
Hamiltonian Systems
Gibbs States
Hydrodynamics
Nearest Neighbor
Crystal
Entropy
Perturbation
Unit
Invariant
Energy

Keywords

  • Mathematics Subject Classification (1991): 60K35, 82A05

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Stationary states of random Hamiltonian systems. / Fritz, J.; Funaki, Tadahisa; Lebowitz, J. L.

In: Probability Theory and Related Fields, Vol. 99, No. 2, 06.1994, p. 211-236.

Research output: Contribution to journalArticle

Fritz, J. ; Funaki, Tadahisa ; Lebowitz, J. L. / Stationary states of random Hamiltonian systems. In: Probability Theory and Related Fields. 1994 ; Vol. 99, No. 2. pp. 211-236.
@article{c0c27c2dbca546bf9a058c126c0dfe73,
title = "Stationary states of random Hamiltonian systems",
abstract = "We investigate the ergodic properties of Hamiltonian systems subjected to local random, energy conserving perturbations. We prove for some cases, e.g. anharmonic crystals with random nearest neighbor exchanges (or independent random reflections) of velocities, that all translation invariant stationary states with finite entropy per unit volume are microcanonical Gibbs states. The results can be utilized in proving hydrodynamic behavior of such systems.",
keywords = "Mathematics Subject Classification (1991): 60K35, 82A05",
author = "J. Fritz and Tadahisa Funaki and Lebowitz, {J. L.}",
year = "1994",
month = "6",
doi = "10.1007/BF01199023",
language = "English",
volume = "99",
pages = "211--236",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Stationary states of random Hamiltonian systems

AU - Fritz, J.

AU - Funaki, Tadahisa

AU - Lebowitz, J. L.

PY - 1994/6

Y1 - 1994/6

N2 - We investigate the ergodic properties of Hamiltonian systems subjected to local random, energy conserving perturbations. We prove for some cases, e.g. anharmonic crystals with random nearest neighbor exchanges (or independent random reflections) of velocities, that all translation invariant stationary states with finite entropy per unit volume are microcanonical Gibbs states. The results can be utilized in proving hydrodynamic behavior of such systems.

AB - We investigate the ergodic properties of Hamiltonian systems subjected to local random, energy conserving perturbations. We prove for some cases, e.g. anharmonic crystals with random nearest neighbor exchanges (or independent random reflections) of velocities, that all translation invariant stationary states with finite entropy per unit volume are microcanonical Gibbs states. The results can be utilized in proving hydrodynamic behavior of such systems.

KW - Mathematics Subject Classification (1991): 60K35, 82A05

UR - http://www.scopus.com/inward/record.url?scp=21344497680&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21344497680&partnerID=8YFLogxK

U2 - 10.1007/BF01199023

DO - 10.1007/BF01199023

M3 - Article

AN - SCOPUS:21344497680

VL - 99

SP - 211

EP - 236

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 2

ER -