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.

The Symmetric Algebra for Certain Monomial Curves

In this article we compute a minimal Groebner basis for the symmetric algebra for certain affine Monomial Curves, as an R-module. Keywords: Monomial Curves, Groebner Basis, Symmetric Algebra. Mathematics Subject Classification 2000: 13P10, 13A30

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