Friction and noise for a probe in a nonequilibrium fluid

Abstract

Abstract. We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid. The problemWhether the environment of a system is in equilibrium or is driven into a nonequilibrium condition is important for characterizing internal motions and reactions. In other words the reduced system dynamics will reflect whether the environment is driven or not.For example, the relation between noise and friction on the system need no longer be described via the standard second fluctuation-dissipation (or Einstein) relation, we cannot unambiguously speak about entropy fluxes into the environment in terms of heat as there would be no Clausius relation, and system fluctuations or noise level in general are not simply quantified by a reservoir temperature. The present paper takes up the challenge of characterizing such an effective dynamics for a probe in contact with a nonequilibrium medium. One should have in mind that the medium consists of active elements or driven particles themselves in contact with a big thermal equilibrium reservoir (like surrounding air or water). Combined, the medium and the heat bath make up the nonequilibrium fluid. The system is called a probe here, but it can in general also refer to a collective or with j = 1, . . . , N labeling the particles and subject to independent standard white noises ξ j t . The β denotes the inverse temperature of the background equilibrium reservoir but the particles are effectively driven by the nonconservative force F . For simplicity we have not introduced explicitly friction and mass parameters, keeping only λ (coupling) and β as parameters. The particle interaction is given through the potential Φ while the potential U depends on the position X t of the probe, thus representing the back-reaction of the probe on each particle. Other and different types of interaction between probe and medium are possible, e.g. in terms of their center of mass coordinate with a mean field type potential U ( j x j t − X t ), here not discussed and inessential for the present level of discussion. Keeping to (1.1) the probe dynamics itself iswhere we indicate by K X t ,Ẋ t other aspects of the probe motion in the fluid. Its mass M is obviously also an important parameter for separation of time-scales between probe and fluid particle motion.The equations (1.1) and (1.2) starting at t = 0 are the basic evolution equations representing the coupled dynamics of probe and fluid particles. Nonequilibrium works directly on the medium which is ...

Frenesy: Time-symmetric dynamical activity in nonequilibria

“…The system responds and that feeds back to the probe motion, making friction and noise. That scenario has been recently investigated in a number of papers starting from nonequilibrium response, [15,[102][103][104].…”

“…At that moment, the notion of entropy production refers to dissipation in a more distant equilibrium reservoir, which is for example thermostatting a nonequilibrium medium to which the particles are coupled. Questions on statistical forces, fluctuation and response behavior and the derivation of Brownian motion induced by contact with nonequilibria are central here [15].…”

Rectification and Non-Gaussian Diffusion in Heterogeneous Media

“…In the first example, we will study the diffusion of particles in an inhomogeneous medium under the influence of a constant force. This case is frequently observed in colloidal suspensions in which particles interact through direct or hydrodynamic interactions, and in diffusion in complex systems [10][11][12][13][14]. As a second case, we will analyze the motion of a Brownian particle moving in a confined medium which induces x-dependent entropic forces [15][16][17][18][19][20][21][22][23][24].…”

“…Substituting Equation (10) into Equation (12) and remembering that χ = 1 when calculated by Equation (11), we obtain:…”

Least-rattling feedback from strong time-scale separation

“…A geometric interpretation of this bound was presented in [6], and extended to nonequilibrium baths in [7], as well as to reversible external protocols in [8]. Systems where slow variables have their own dynamics under a conservative coupling to the fast bath have received relatively little attention, excepting notable recent work for a simple harmonic oscillator probe in [9], and a more general exploration in [10,11], where some formal results relating dissipation and forces on the slow variables were derived.…”