Hydrodynamic (non-equil.) FIF

red ball Non-equilibrium steady states generically lead to power-law correlations for conserved quantities.

Are there associated FIF, e.g. for a fluid confied between plates at different temperatures?

yellow ball "Giant Casimir Effect in Fluids in Nonequilibrium Steady States,"

T. R. Kirkpatrick, J. M. Ortiz de Zárate, and J. V. Sengers, Phys. Rev. Lett. 110, 235902 (2013):

Fluctuating hydrodynamics predicts long-range correlated temperature/density fluctuations. Pressure is locally argued to be:

Evaluating the non-equilibrium contributions to the fluctuations, results in

red ball Inclusion of 3 conserved quantities (number, momentum, energy) makes it difficult to test the above .

yellow ball A simpler example involves diffusion between reservoirs at different densities; i.e.a steady state with uniform current flow.

 "Fluctuation-induced forces in Non-equilibrium (difusive) dynamics,"

Avi Aminov, Yariv Kafri, and M. Kardar, arXiv:1501.01006 (2015):

 

The presence of a current leads to large, position dependent, fluctuations in density.

Density fluctuations are different on the 2 sides of each plate, leading to a net force

yellow ball The amplitude is non-universal, and dependent on dynamics.

yellow ball The force can be attractive (hard core particles, below) or repulsive.

yellow ball What is the FIF between compact objects immersed in the diffusing current?