Dynamics of a massive piston in an ideal gas

N. I. Chernov, J. L. Lebowitz, Ya G. Sinai

Research output: Contribution to journalReview articlepeer-review

20 Scopus citations


This survey is a study of a dynamical system consisting of a massive piston in a cubic container of large size L filled with an ideal gas. The piston has mass M ∼ L2 and undergoes elastic collisions with N ∼ L3 non-interacting gas particles of mass m = 1. It is found that under suitable initial conditions there is a scaling regime with time and space scaled by L in which the motion of the piston and the one-particle distribution of the gas satisfy autonomous coupled equations (hydrodynamic equations) such that in the limit L → ∞ the mechanical trajectory of the piston converges in probability to the solution of the hydrodynamic equations for a certain period of time. There is also a heuristic discussion of the dynamics of the system on longer intervals of time.

Original languageEnglish (US)
Pages (from-to)1045-1125
Number of pages81
JournalRussian Mathematical Surveys
Issue number6
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • General Mathematics


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