Scaling Dynamics of a Massive Piston in a Cube Filled With Ideal Gas Exact Results.pdf

2 0 0 2 c Scaling Dynamics of a Massive Piston in a Cube e D Filled With Ideal Gas: Exact Results 0 3 1,4 2,4 3 ] N. Chernov , J. L. Lebowitz , and Ya. Sinai h c e February 1, 2008 m - t a t Dedicated to Robert Dorfman on the occasion of his 65th birthday s . t a Abstract m - We continue the study of the time evolution of a system consisting of a piston d n in a cubical container of large size L filled with an ideal gas. The piston has o mass M ∼ L2 and undergoes elastic collisions with N ∼ L3 gas particles of mass c m. In a previous paper, Lebowitz, Piasecki and Sinai [LPS] considered a scaling [ regime, with time and space scaled by L, in which they argued heuristically that the 1 v motion of the piston and the one particle distribution of the gas satisfy autonomous 7 coupled differential equations. Here we state exact results and sketch proofs for 3 this behavior. 6 2 1 2 1 The model and main results 0 / t This paper is a continuation of [LPS], where deterministic scaled equations describing the a m dynamics of a massive piston in a cubical container filled with ideal gas were given. Here d- we state exact conditions on the validity of those equations and outline the arguments. n Full proofs will be published in a separate paper [CLS]. o We refer the reader to [LPS] and to [CLS] as well as [G, GF, GP, KBM, Li] for a c : detailed descri