Thermal Fluctuation-Induced Pressure
Equilibrium (Critical or Goldstone)
Finite-size behavior of free energy confined between plates takes a universal form at criticality
M.E. Fisher and P.-G. de
Gennes, C. R. Acad. Sci. Ser. B 287, 207 (1978)
Experimental confirmation for colloidal particles in critical oil/water mixture.
Hertlein,
Helden, Gambassi, Dietrich & Bechinger, Nature 451, 172
(2008)
Goldstone mode fluctuations following continuous symmetry breaking are long-range correlated
H. Li . Kardar, Phys.
Rev. Lett. 67, 3275 (1991)
Experimental confirmation in wetting of superfluid films
R. Garcia and M.H.W. Chan,
Phys. Rev. Lett. 83, 1187 (1999)
Non-equilibrium steady states?
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 Casimir force?
Fluctuating hydrodynamics predicts long-range correlated temperature/density fluctuations.
H. Wada, and S.-i. Sasa, Phys. Rev. E 67, 065302 (2003) [arxiv] (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
Presence of 3 conserved quantities (number, momentum, energy) makes it difficult to numerically confirm the above.