Non-equilibrium Pressure
Radiation Pressure in a non-equilibrium steady state with different temperatures
"Surface Phonon Polaritons Mediated Energy Transfer between Nanoscale Gaps," S.Shen, A. Narayanaswamy, & G. Chen, Nano Lett. 9, 2909 (2009) Breaking the law, at the nanoscale (MIT news, July 29, 2009)
A generalized approach for computation of Casimir forces, as well as radiation and heat transfer.
"Nonequilibrium Electromagnetic Fluctuations: Heat Transfer and Interactions,"
M. Krüger, T. Emig, and M. Kardar, Phys. Rev. Lett. 106, 210404 (2011)
Rytov (1959): 
"Fluctuational QED"
Fluctuating currents in each object are related to its temperature by a fluctuation-dissipation condition:
The EM field due to thermal fluctuations of one object is related to overall Green's function by:
The overall fluctuations with many objects at different temperatures is then given by:
From EM correlations follow the stress tensor and the Poynting vector, hence forces and radiation.
Particles? Long-range (and universal) Casimir forces arise from long-range correlated (quantum or thermal) fluctuations.
Non-equilibrium fluctuations of conserved quantities can be long-ranged.
Is there a corresponding universal Casimir force?
Fluctuating hydrodynamics predicts long-range correlated temperature/density fluctuations.
H. Wada, and S.-i. Sasa, Phys. Rev. E 67, 065302 (2003) (Fluctuating shear flow)
T. R. Kirkpatrick, J. M. Ortiz de Zárate, and J. V. Sengers, Phys. Rev. Lett. 110, 235902 (2013): (Temperature gradient)
Pressure is locally argued to be:
Evaluating the non-equilibrium contributions to the fluctuations, results in
The presence of 3 conserved quantities (number, momentum, energy) makes it difficult to numerically confirm the above predictions.
Diffusive Pressure? 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, Phys. Rev. Lett. 114, 230602 (2015):
ρl 
ρr
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