Statistical mechanics of stationary states. I. Formal theory

Abstract

In this paper a microscopic theory for the nonequilibrium average of any dynamical variable, and of fluctuations in particular, is presented. The general theory is specialized to nonequilibrium stationary states (NESS) of simple fluids. It is found that the fluctuations around the NESS are qualitatively different from equilibrium fluctuations. There appears a coupling between the fluctuations and the macroscopic dissipative fluxes, linked to a breaking of time-reversal symmetry. The dynamic structure factor is analyzed in a heat-transporting NESS and is found to be ${S_{\overrightarrow{k}\omega }}^{=} {S_{\overrightarrow{k}\omega }}^{\mathrm{hom}}+i\xi (k,\omega )\overrightarrow{\mathrm{k}}·\overrightarrow{\nabla }\beta \mathit{\Phi }+\alpha (k,\omega )\overrightarrow{\mathrm{k}}·\overrightarrow{\nabla }\beta \mathit{\Phi }$, where the first term is the one predicted by local equilibrium theory and is even in $\overrightarrow{\mathrm{k}}$ and $\omega$, the second is even in $\omega$ and odd in $\overrightarrow{\mathrm{k}}$, and the third is odd in $\overrightarrow{\mathrm{k}}$ and in $\omega$. Possible light-scattering experiments for measuring the new effects are discussed.