Speaker
Prof.
Ryoichi Kawai
(University of Alabama at Birmingham)
Description
A Brownian piston separating two gases of different
temperature mediates heat transfer from one gas to the other
via its velocity fluctuations. Such heat transfer is well
understood at the Langevin theory. However, the gases in
turn exert non-equilibrium force on the piston. Such a
force is responsible for various intriguing non-equilibrium
processes such as adiabatic piston and a certain types of
Brownian motors. It has been shown that the standard linear
Langevin theory fails to explain the force. The
Master-Boltzmann approach beyond the Langevin description
successfully predicted the force but it did not reveal the
physical origin of the force. Recently, Freleux et al [PRL 108,
160601 (2012)] introduced the new concept of momentum
deficit due to dissipation (MDD) and showed that it can
explain the origin of the force with a few lines of
calculation only based on the energy and momentum
conservation laws.
However, all previous theories including the MDD assume that
the gas particles hitting the piston are taken from an
equilibrium velocity distribution and outgoing particles
disappears without colliding with the incoming particles.
Since the outgoing particles are not in a thermal
equilibrium due to dissipation, their collision with the
incoming particles disturbs the velocity distribution of the
incoming
particles, invalidating the assumption used in the previous
theories. Therefore, I would like to discuss the MDD from the
hydrodynamics point of view. When a nonequilibrium steady
state is established, we can show that the heat and momentum
fluxes in the gases satisfy the MDD condition
such that energy and momentum transport in hydrodynamics is
consistent with the MDD theory of adiabatic piston.
