The periodic oscillation of an adiabatic piston in two or three dimensions ∗ preprint
نویسنده
چکیده
We study a heavy piston of mass M that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system’s averaged equation and showed that its solutions oscillate periodically. Using averaging techniques, we prove that the actual motions of the piston converge in probability to the predicted averaged behavior on the time scale M1/2 when M tends to infinity while the total energy of the system is bounded and the number of gas particles is fixed. Mathematics Subject Classification (2000): 34C29, 37A60, 82C22.
منابع مشابه
The Adiabatic Piston and the Second Law of Thermodynamics
Abstract. A detailed analysis of the adiabatic-piston problem reveals peculiar dynamical features that challenge the general belief that isolated systems necessarily reach a static equilibrium state. In particular, the fact that the piston behaves like a perpetuum mobile, i.e., it never stops but keeps wandering, undergoing sizable oscillations, around the position corresponding to maximum entr...
متن کاملThe adiabatic piston: a perpetuum mobile in the mesoscopic realm
A detailed analysis of the adiabatic-piston problem reveals, for a finely-tuned choice of the spatial dimensions of the system, peculiar dynamical features that challenge the statement that an isolated system necessarily reaches a time-independent equilibrium state. In particular, the piston behaves like a perpetuum mobile, i.e., it never comes to a stop but keeps wandering, undergoing sizeable...
متن کاملDynamical aspects of an adiabatic piston.
Dynamical aspects of an adiabatic piston are investigated, based on the mass ratio expansion of the master equation for the piston velocity distribution function. Simple theory for piston motion and relaxation of an ideal gas in a cylinder turns out to reproduce our numerical experiments quantitatively.
متن کاملFrom the adiabatic piston to macroscopic motion induced by fluctuations
The controversial problem of the evolution of an isolated system with an internal adiabatic wall is investigated with the use of a simple microscopic model and the Boltzmann equation. In the case of two infinite volume onedimensional ideal fluids separated by a piston whose mass is equal to the mass of the fluid particles we obtain a rigorous explicit stationary non-equilibrium solution of the ...
متن کاملDissipative collapse of the adiabatic piston
– An adiabatic piston, separating two granular gases prepared in the same macro-scopic state, is found to eventually collapse to one of the sides. This new instability is explained by a simple macroscopic theory which is furthermore in qualitative agreement with hard disk molecular dynamics. The problem of the so-called adiabatic piston was described in 1960 by Callen [1] and has received a lot...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006