Nonequilibrium Fluctuation-Induced Interactions
Are there long-ranged fluctuation-induced interactions in active matter?
"Fluctuation-Induced Casimir Forces in Granular Fluids,"
C. Cattuto, R. Brito, U.M.B. Marconi, F. Nori, and R. Soto, Phys. Rev. Lett. 96, 178001 (2006)
"Nonadditivity of Fluctuation-Induced Forces in Fluidized Granular Media,"
M.R. Shaebani1, J. Sarabadani, and D.E. Wolf, Phys. Rev. Lett. 108, 198001 (2012)
"Casimir effect in actice mtter systems,"
D. Ray, C. Reichhardt, and C.J. Olson Reichhardt, Phys. Rev. E 90, 013019 (2014)
The answer is negative: no long-ranged correlations and no long-ranged interactions.
Agitating active matter from rest:
C.M. Rohwer, M. Kardar and Matthias Krüger, PRL 188, 015702 (2017)
Self-propelled colloidal particles Shaken Grains
Fluctuations of the conserved density field satisfy (model B):
Resulting in the trivial (uncorrelated) steady state
What happens when the level of activity/noise is suddently changed (quench) with confining plates?
The assumption of local equilibrium suggests a time-varying pressure on each plate:
The density fluctuations on the two sides of plates in a parallel plate geometry are different.
In a Gaussian model, the second term leads to transient universal long-range fluctuation-induced force:
Simulations of Active Brownian Particles agitated (from rest) between walls separated by L:
Active particles condense on a repulsive surface!
The evolution of the mean density profile leads to an additonal (calculable) contribution from the first term.
Simulations results for an interacting gas (initial condition corresponding to infinite temperature):
The transient force due to relaxation of the mean density profile decays with time exponentially
The long time decay of the force is due to the (repulsive) contribution of transient density fluctuations.
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.
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)
Steady state fluctuation force: Consider diffusion between reservoirs at different densities; i.e. a steady state with a uniform current.
"Fluctuation-induced forces in Non-equilibrium (difusive) dynamics," Aminov, Kafri, & M.K., PRL 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
Conserved density leads to long-ranged correlations and interactions out of equilibrium.
Transient fluctuation-induced force between two inclusions:
