Non-equilibrium Steady States

red ball  Long-range (and universal) Casimir forces arise from long-range correlated (quantum or thermal) fluctuations.

yellow ballNon-equilibrium fluctuations of conserved quantities can be long-ranged.

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)

Is there a corresponding universal Casimir force?

red ball 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

yellow ballThe presence of a current leads to correlated, position dependent, fluctuations in density.

yellow ballDensity 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

yellow ballWe tested this prediction numerically:

yellow ballMore 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

yellow ball For plates a different temperatures,Kirkpatrick et al  argue for a fluctuation-induced force:

red ballRadiation Pressure arises in a non-equilibrium steady state with different temperatures


yellow ball "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)

red ballA generalized approach for computation of Casimir forces, as well as radiation and heat transfer.

yellow ball "Nonequilibrium Electromagnetic Fluctuations: Heat Transfer and Interactions,"

M. Krüger, T. Emig, and M. Kardar, Phys. Rev. Lett. 106, 210404 (2011)

Rytov (1959):      "Fluctuational QED"

yellow ball Fluctuating currents in each object are related to its temperature by a fluctuation-dissipation condition:

yellow ball The EM field due to thermal fluctuations of one object is related to overall Green's function by:

yellow ball The overall fluctuations with many objects at different temperatures is then given by:

yellow ball From EM correlations follow the stress tensor and the Poynting vector, hence forces and radiation.