We apply the concept of a frequency-dependent effective temperature based on the fluctuationdissipation ratio to a driven Brownian particle in a nonequilibrium steady state. Using this system as a thermostat for a weakly coupled harmonic oscillator, the oscillator thermalizes according to a canonical distribution at the respective effective temperature across the entire frequency spectrum. By turning the oscillator from a passive "thermometer" into a heat engine, we realize the cyclic extraction of work from a single thermal reservoir, which is feasible only due to its nonequilibrium nature.Introduction. -Cornerstone principles of equilibrium statistical mechanics, such as the equipartition of energy or the fluctuation-dissipation theorem (FDT) [1], are generally not directly applicable to ageing (e.g., glasses [2]) or driven systems (e.g., active particles [3][4][5]). Sometimes equilibrium relations can be reconciled by introducing an "effective" quantity that compensates for nonequilibrium deviations. In this spirit, the FDT can be formally maintained by interpreting the fluctuation-dissipation ratio (FDR) as an effective temperature [6][7][8][9]. However, a nonequilibrium FDR may depend on both time and the choice of observable, which is fundamentally at odds with the properties of an equilibrium temperature. This caveat has led to the common notion that the effective temperature acquires thermodynamical meaning only if these dependencies are not too pronounced or can be appropriated to separate length-and/or time scales [2,[8][9][10][11][12].For this reason, the effective temperature concept has been so prolific in describing the nonequilibrium properties of glassy systems [7,9]. While fast vibrational fluctuations remain equilibrated with the environment, the slow evolution of the out-of-equilibrium structure is characterized by a higher effective temperature, a scenario known as partial equilibration [7]. During the ageing process, this effective temperature slowly decreases until eventually the environmental temperature is reached on all time scales [2,13]. However, in complex fluids or biological matter this kind of dynamical time-scale separation is the exception rather than the rule. In this regime of mixed time scales, time-dependent FDRs have been studied, i.a., for active matter [5,11,[14][15][16][17][18][19], sheared colloidal suspensions [10,20,21] and single biomolecules [12]. In a heuristic approach introduced in the glassy context [2,7] and revisited for driven Brownian [15,16,22] and ageing [23] systems, the effective temperature is identified with the measurement by a thermometer. However, while in equilibrium any conceivable thermometer must read the same temperature, this is no longer true in the nonequilibrium case, where time scales

Entropic depletion forces arise between mesoscopic bodies that are immersed in a suspension of macromolecules, such as colloid-polymer mixtures. Here we consider the case of a driven colloidal probe in the presence of another, passive colloidal particle, both solvated in an ideal bath of small spherical particles. We calculate the nonequilibrium forces mediated by the depletants on the two colloidal particles within a dynamical superposition approximation (DSA) scheme. In order to assess the quality of this approximation, and to obtain the colloidal microstructure around the driven probe, we corroborate our theoretical results with Brownian dynamics simulations.

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Employing theory and numerical simulations, we demonstrate discontinuous force thinning due to the driven motion of an external probe in a host medium. We consider two cases: an ideal structureless medium (modeling ultrasoft materials such as polymer melts) and a dilute bath of interacting repulsive particles. When the driving of the probe exceeds a critical force, the microviscosity of the medium drops abruptly by about an order of magnitude. This phenomenon occurs for strong attractive interactions between a large probe and a sufficiently dense host medium.

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