Learn More
An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt (threshold of deterministic running solutions) a scaling behavior for weak thermal noise is revealed and various(More)
Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full(More)
The effective diffusion coefficient for the overdamped Brownian motion in a tilted periodic potential is calculated in closed analytical form. Universality classes and scaling properties for weak thermal noise are identified near the threshold tilt where deterministic running solutions set in. In this regime the diffusion may be greatly enhanced, as(More)
The total entropy production of a trajectory can be split into an adiabatic and a nonadiabatic contribution, deriving, respectively, from the breaking of detailed balance via nonequilibrium boundary conditions or by external driving. We show that each of them, the total, the adiabatic, and the nonadiabatic trajectory entropy, separately satisfies a detailed(More)
We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by <W{diss}> =W-DeltaF=kTD(rho||rho[over ])=kT<ln(rho/rho[over ])>, where rho and rho[over ] are the phase-space density of the(More)
We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform(More)
We study the efficiency at maximum power, η*, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For engines reaching Carnot efficiency ηC=1-Tc/Th in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that η* is bounded from above by(More)
– We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density P (W) of the work W performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres. Exactly solvable(More)
We elucidate the connection between various fluctuation theorems by a microcanonical version of the Crooks relation. We derive the microscopically exact expression for the work distribution in an idealized Joule experiment, namely, for a convex object moving at constant speed through an ideal gas. Analytic results are compared with molecular dynamics(More)