Diffusive Pressure

 With 3 conserved quantities (N, p, E) it is difficult to numerically confirm fluctuating hydrodynamic predictions.

 A simpler system 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 correlated, position dependent, fluctuations in density.

Density fluctuations are different on the 2 sides of each plate, leading to a position-dependent pressure

For the Symmetric Simple Exclusion Process (SSEP) in two dimensions

We tested this prediction numerically:

More generally, for small density gradients:

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

 The force can be attractive (SSEP) or repulsive.

 The same (non-extensive) form is obtained in higher dimensions

 What is the fluctuation-induced force (FIF) between compact objects immersed in the diffusing current?

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