Shear-driven heat flow in absence of a temperature gradient

Abstract

Jaynesian statistical inference is used to predict that steady, non-uniform Couette flow in a simple liquid will generate a heat flux proportional to the gradient of the square of the strain-rate when the temperature gradient is negligible. The heat flux is divided into phonon and self-diffusion components, with the latter coupling to the elastic strain and inelastic strain-rate. Operators for all these are substituted into the information-theoretic phase-space distribution. By taking moments of an exact equation for this distribution derived by Robertson, one obtains an evolution equation for the self-diffusion component of the heat flux which, in a steady state, predicts shear-driven heat flow.