Active Brownian particles: Entropy production and fluctuation-response

Within the Rayleigh-Helmholtz model of active Brownian particles activity is due to a non-linear velocity dependent force. In the presence of an external trapping potential or a constant force, the steady state of the system breaks detailed balance producing a net entropy. Using molecular dynamics simulations, we obtain the probability distributions of entropy production in these steady states. The distribution functions obey detailed fluctuation theorem for entropy production. Using simulation results, we further show that the steady state response function obeys a modified fluctuation-dissipation relation.Comment: 8 pages, 6 figures; version accepted for publication in Phys. Rev.

Stochastic models of classical particle pumps : Density dependence of directed current

We present and compare different versions of a simple particle pump-model that describes average directed current of repulsively interacting particles in a narrow channel, due to time-varying local potentials. We analyze the model on discrete lattice with particle exclusion, using three choices of potential-dependent hopping rates that obey microscopic reversibility. Treating the strength of the external potential as a small parameter with respect to thermal energy, we present a perturbative calculation to obtain the expression for average directed current. This depends on driving frequency, phase, and particle density. The directed current vanishes as density goes to zero or close packing. For two choices of hopping rates, it reaches maximum at intermediate densities, while for a third choice, it shows a curious current reversal with increasing density. This can be interpreted in terms of a particle-hole symmetry. Stochastic simulations of the model show good agreement with our analytic predictions.Comment: 9 pages, 1 figure: Based on invited talk delivered by the author at StatPhys-Kolkata VIII, Kolkata (India), December, 201

Stochastic ratcheting of two dimensional colloids : Directed current and dynamical transitions

We present results of molecular dynamics simulations for two-dimensional repulsively interacting colloids driven by a one dimensional asymmetric and commensurate ratchet potential, switching on and off stochastically. This drives a time-averaged directed current of colloids, exhibiting resonance with change in ratcheting frequency, where the resonance frequency itself depends non-monotonically on density. Using scaling arguments, we obtain analytic results that show good agreement with numerical simulations. With increasing ratcheting frequency, we find non-equilibrium re-entrant transitions between solid and modulated liquid phases.Comment: paper and supplementary; published versio

Mechanical Failure of a Small and Confined Solid

Starting from a commensurate triangular thin solid strip, confined within two hard structureless walls, a stretch along its length introduces a rectangular distortion. Beyond a critical strain the solid fails through nucleation of "smectic"-like bands. We show using computer simulations and simple density functional based arguments, how a solid-smectic transition mediates the failure. Further, we show that the critical strain introducing failure is {\em inversely} proportional to the channel width i.e. thinner strips are stronger!Comment: 6 pages, 7 figures, to be published in Indian Journal of Physics (in press) as a Conference proceeding of CMDAYS-0

Stochastic thermodynamics of active Brownian particles

Examples of self propulsion in strongly fluctuating environment is abound in nature, e.g., molecular motors and pumps operating in living cells. Starting from Langevin equation of motion, we develop a fluctuating thermodynamic description of self propelled particles using simple models of velocity dependent forces. We derive fluctuation theorems for entropy production and a modified fluctuation dissipation relation, characterizing the linear response at non-equilibrium steady states. We study these notions in a simple model of molecular motors, and in the Rayleigh-Helmholtz and energy-depot model of self propelled particles.Comment: 8 pages, version accepted in Phys. Rev.

Modified fluctuation-dissipation and Einstein relation at non-equilibrium steady states

Starting from the pioneering work of G. S. Agarwal [Zeitschrift f\"ur Physik 252, 25 (1972)], we present a unified derivation of a number of modified fluctuation-dissipation relations (MFDR) that relate response to small perturbations around non-equilibrium steady states to steady-state correlations. Using this formalism we show the equivalence of velocity forms of MFDR derived using continuum Langevin and discrete master equation dynamics. The resulting additive correction to the Einstein relation is exemplified using a flashing ratchet model of molecular motors.Comment: 7 pages, 3 figures; accepted for publication in Phys Rev