Fluctuation Induced Forces in Non-equilibrium (Diffusive) Dynamics

Aminov, A. N.; Kafri, Yariv; Kardar, Mehran

doi:10.48550/arxiv.1501.01006

Cited by 2 publications

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“…Some authors have proposed NE Casimir forces induced by long-range fluctuations that originate from the spatial dependence of the noise correlations associated with the local fluctuation-dissipation theorem in the presence of a gradient [36,37]. However, for fluids it has been found that these NE correlations are insignificant compared to the NE correlations caused by a coupling between hydrodynamic modes in NE states considered here [38].…”

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confidence: 90%

Nonequilibrium Casimir-like Forces in Liquid Mixtures

2015

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In this Letter, we consider a liquid mixture confined between two thermally conducting walls subjected to a stationary temperature gradient. While in a one-component liquid nonequilibrium fluctuation forces appear inside the liquid layer, nonequilibrium fluctuations in a mixture induce a Casimir-like force on the walls. The physical reason is that the temperature gradient induces large concentration fluctuations through the Soret effect. Unlike temperature fluctuations, nonequilibrium concentration fluctuations are also present near a perfectly thermally conducting wall. The magnitude of the fluctuation-induced Casimir force is proportional to the square of the Soret coefficient and is related to the concentration dependence of the heat and volume of mixing. When large and long-range fluctuations are present, they will induce forces in confined fluids [1]. These are commonly referred to as Casimir-like forces in analogy to forces induced by vacuum fluctuations between two conducting plates [2,3]. A well-known example is the Casimir force induced by critical fluctuations in fluids [4][5][6][7]. Apart from critical systems, long-range correlations also exist in equilibrium systems with Goldstone modes [1] and in many nonequilibrium systems, where even longerrange correlations can exist [8][9][10][11].In this Letter, we consider a liquid mixture in a nonequilibrium steady state (NESS) between two parallel thermally conducting plates subjected to a uniform temperature gradient ∇T. In a liquid mixture a temperature gradient induces large concentration fluctuations through the Soret effect [12,13]. These nonequilibrium concentration fluctuations vary with the 4th power of the inverse of the wave number k of the fluctuations, just as the nonequilibrium temperature fluctuations in a one-component fluid [8,14]. However, there is a principal difference between the Casimir pressures induced by nonequilibrium concentration fluctuation and those induced by nonequilibrium temperature fluctuations. In thin fluid layers, fluctuations not only may induce a force on the walls, but also may introduce an effective potential inside the fluid layer causing a modification of the density or composition profile [15]. While in a one-component fluid nonequilibrium fluctuations induce the latter phenomenon yielding a rearrangement of the density profile [16], the purpose of the present Letter is to demonstrate that nonequilibrium concentration fluctuations induce an actual Casimir pressure on the walls directly.It is well known that in considering the dynamics of fluctuations around thermal equilibrium, nonlinear terms in the hydrodynamic equations serve to renormalize various terms in the linearized hydrodynamic equations [17][18][19][20][21][22][23][24].Here we show that in a NESS the nonlinear terms cause a most important renormalization of the nonequilibrium (NE) pressure or normal stresses in a binary fluid. To determine the nonequilibrium induced pressure in a liquid mixture, we need to consider the pressure p as a function of the fl...

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confidence: 90%

Nonequilibrium Casimir-like Forces in Liquid Mixtures

2015

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“…For interacting particles in the media with generic long range correlations, that effect can only be enhanced and other issues become also important. Indeed, as a related effect for spatially extended systems, the difference between bulk and boundary contributions to statistical forces is fading [4]. All that is relevant for the status and possibility of steady state thermodynamics, the macroscopic theory of nonequilibrium systems.…”

Section: Kinetic Aspectsmentioning

confidence: 99%

“…It is of much current interest to extend the study of statistical forces to nonequilibrium regimes [4][5][6]. There are multiple motivations beyond the general ambition of constructing a nonequilibrium statistical mechanics.…”

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How Statistical Forces Depend on the Thermodynamics and Kinetics of Driven Media

2015

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We study the statistical force of a nonequilibrium environment on a quasistatic probe. In the linear regime, the isothermal work on the probe equals the excess work for the medium to relax to its new steady condition with a displaced probe. Also, the relative importance of reaction paths can be measured via statistical forces, and from second order onwards the force on the probe reveals information about nonequilibrium changes in the reactivity of the medium. We also show that statistical forces for nonequilibrium media are generally nonadditive, in contrast with the equilibrium situation. Both the presence of nonthermodynamic corrections to the forces and their nonadditivity put serious constraints on any formulation of nonequilibrium steady state thermodynamics.

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Fluctuation Induced Forces in Non-equilibrium (Diffusive) Dynamics

Cited by 2 publications

References 0 publications

Nonequilibrium Casimir-like Forces in Liquid Mixtures

Nonequilibrium Casimir-like Forces in Liquid Mixtures

How Statistical Forces Depend on the Thermodynamics and Kinetics of Driven Media

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