Effective temperature of active matter

Effective temperature of red-blood-cell membrane fluctuations

Biologically driven nonequilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures theoretically by examining a randomly kicked particle, with a variable number of kicking motors, and show how these two indicators of nonequilibrium behavior can contradict. Our results are compared with new experiments on shape fluctuations of red-blood cell membranes, and demonstrate how the physical nature of the motors in this system can be revealed using these global measures of nonequilibrium.

Sedimentation and effective temperature of active colloidal suspensions

In this Letter, we investigate experimentally the nonequilibrium steady state of an active colloidal suspension under gravity field. The active particles are made of chemically powered colloids, showing self propulsion in the presence of an added fuel, here hydrogen peroxide. The active suspension is studied in a dedicated microfluidic device, made of permeable gel microstructures. Both the microdynamics of individual colloids and the global stationary state of the suspension under gravity are measured with optical microscopy. This yields a direct measurement of the effective temperature of the active system as a function of the particle activity, on the basis of the fluctuation-dissipation relationship. Our work is a first step in the experimental exploration of the out-of-equilibrium properties of active colloidal systems.

Motor-driven effective temperature and viscoelastic response of active matter

We consider dynamic response of a cytoskeletal network to both thermal and motor-induced fluctuations. The latter are viewed in two independent ways, as either additive or multiplicative colored noise. Due to a natural upper frequency limit of the motor agitation, the response of a living cell is similar to that of an equilibrium system in the high-frequency domain. At lower frequencies, the role of motor agitation manifests itself in intensified network fluctuations, which is equivalent to effective growth of the environment temperature. The effective temperature becomes frequency dependent, which signifies violation of the conventional fluctuation-dissipation theorem. The motor action affects the dynamic shear modulus in two opposite ways: by stiffening the network through filament prestress and softening it through increased agitation. The latter tendency is isolated when only single-headed motors are present. The theory is in good agreement with experimental measurements of the amplitude of the shear modulus under these conditions.

Entropy-based characterizations of the observable dependence of the fluctuation-dissipation temperature

The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable independence is deeply related to the uniformity of the phase-space probability distribution on the hypersurfaces of constant energy. This property is shown explicitly on three different stochastic models, where observable dependence of the fluctuation-dissipation temperature arises only when the uniformity of the phase-space distribution is broken. The first model is an energy transport model on a ring, with biased local transfer rules. In the second model, defined on a fully connected geometry, energy is exchanged with two heat baths at different temperatures, breaking the uniformity of the phase-space distribution. Finally, in the last model, the system is connected to a zero temperature reservoir, and preserves the uniformity of the phase-space distribution in the relaxation regime, leading to an observable-independent temperature.

Dependence of the fluctuation-dissipation temperature on the choice of observable

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is nonuniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely, the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.

Motor-mediated alignment of microtubules in semidilute mixtures

We propose and study a model of molecular motor-induced ordering in a cytoskeletal filament solution for the semidilute case. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. In the semidilute regime multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. The motors, on the one hand, cause closer filament alignment, and, on the other hand, induce fluctuations that are dependent on the relative orientation of the filaments to which the motors are attached. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. This model considers each filament to be in motor contact with all other filaments in the solution. We show that the transition to the oriented state changes from second order to first order when the force-dependent detachment becomes important.