Hydrodynamic Fluctuations around Nonequilibrium Steady State

Abstract

In order to examine the validity of Einstein's fluctuation formula in nonequilibrium situations, hydrodynamic fluctuations in a model syste,m wh.ich can exhibit thermal instability are investigated. Calculations are based on hydrodynamic equations with appropriate fluctuating forces. Neither an incompressibility assumption nor the Boussinesq approximation are adopted in order that the calculated fluctuations at thermal equilibrium may obey the Einstein formula. It is confirmed that the fluctuations associated with' a subsystem whose linear dimension is smaller than a certain characteristic length but is still macroscopic obey the Einstein formula throughout the subcritical.region. On the other hand, certain fluctua­ tions with wavelength comparable to the thickness of the fluid layer are shown to be strongly enhanced near the convection threshold, which is in agreement with Zaitsev and Shliomis' calculation. Therefore, in a nonequilibrium steady state, .our system is practically in thermal equilibrium locally but may be far from it globally as far as the probability of fluctuation is concerned.