Symmetric Brownian motor

Overdamped stochastic thermodynamics with multiple reservoirs

After establishing stochastic thermodynamics for underdamped Langevin systems in contact with multiple reservoirs, we derive its overdamped limit using timescale separation techniques. The overdamped theory is different from the naive theory that one obtains when starting from overdamped Langevin or Fokker-Planck dynamics and only coincides with it in the presence of a single reservoir. The reason is that the coarse-grained fast momentum dynamics reaches a nonequilibrium state, which conducts heat in the presence of multiple reservoirs. The underdamped and overdamped theory are both shown to satisfy fundamental fluctuation theorems. Their predictions for the heat statistics are derived analytically for a Brownian particle on a ring in contact with two reservoirs and subjected to a nonconservative force and are shown to coincide in the long-time limit.

Landauer's blowtorch effect as a thermodynamic cross process: Brownian cooling

The local heating of a selected region in a double-well potential alters the relative stability of the two wells and gives rise to an enhancement of population transfer to the cold well. We show that this Landauer's blowtorch effect may be considered in the spirit of a thermodynamic cross process linearly connecting the flux of particles and the thermodynamic force associated with the temperature difference and consequently ensuring the existence of a reverse cross effect. This reverse effect is realized by directing the thermalized particles in a double-well potential by application of an external bias from one well to the other, which suffers cooling.

Thermally driven Casimir ratchet-oscillator system

We study a fluctuation-driven ratchet-oscillator system that consists of two ratchet pinions in contact with thermal baths at different temperatures. Coupling between noncontact parts of the system is mediated by the Casimir force through a thin corrugated plate. Due to mutual rectification, the two ratchets achieve directed average motion in opposite directions. We numerically probe the average velocity, the Peclet number, and the thermal efficiency of the system as functions of the effective temperatures of the thermal baths and other important dimensionless control parameters. It is found that optimal parameter values exist which maximize the directed transport rate but with very low efficiency. We expect that the obtained results will help in the design of noncontact mechanical devices in the future.

Thermal Brownian motor coupled by Casimir interaction

We study a Feynman-like thermal Brownian motor, in which the asymmetric corrugated cylinder as the ratchet is coupled with a corrugated plate by the noncontact Casimir interaction between them. The source of driving of the system is the thermal fluctuations and its dynamic evolution is described by a set of Langevin equations. Further, the mean velocity and thermal efficiency of the motor in the overdamped limit are studied in detail as a function of the temperature of the baths, external load applied, magnitude of the Casimir interaction, and other relevant parameters by the numerical stimulation. The transport properties attained here and the essential roles of the Casimir interaction can be explicitly demonstrated by designing a Casimir Brownian motor with present nanotechnology.

Brownian pump powered by a white-noise flashing ratchet

A Brownian pump of particles powered by a stochastic flashing ratchet mechanism is studied. The pumping device is embedded in a finite region and bounded by particle reservoirs. In the steady state, we exactly calculate the spatial density profile, the concentration ratio between both reservoirs and the particle flux. We propose a simulation framework for the consistent evaluation of such observable quantities.

Two simple models of classical heat pumps

Motivated by recent studies of models of particle and heat quantum pumps, we study similar simple classical models and examine the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we study do not have particle transport. We consider a two-spin system and a coupled oscillator system which exchange heat with multiple heat reservoirs and which are acted upon by periodic forces. The simplicity of our models allows accurate numerical and exact solutions and unambiguous interpretation of results. We demonstrate that while both our models seem to be built on similar principles, one is able to function as a heat pump (or engine) while the other is not.

Tight coupling in thermal Brownian motors

We study analytically a thermal Brownian motor model and calculate exactly the Onsager coefficients. We show how the reciprocity relation holds and that the determinant of the Onsager matrix vanishes. Such a condition implies that the device is built with tight coupling. This explains why Carnot's efficiency can be achieved in the limit of infinitely slow velocities. We also prove that the efficiency at maximum power has the maximum possible value, which corresponds to the Curzon-Alhborn bound. Finally, we discuss the model acting as a Brownian refrigerator.

Heat fluctuations in Brownian transducers

The heat fluctuation probability distribution function in Brownian transducers operating between two heat reservoirs is studied. We find, both analytically and numerically, that the recently proposed fluctuation theorem for heat exchange [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)] has to be applied carefully when the coupling mechanism between both baths is considered. We also conjecture how to extend such a relation when an external work is present.

Thermal Brownian motor

Recently, a thermal Brownian motor was introduced (Van den Broeck et al 2004 Phys. Rev. Lett. 93 090601), for which an exact microscopic analysis is possible. The purpose of this paper is to review some further properties of this construction, and to discuss in particular specific issues including the relation with macroscopic response and the efficiency at maximum power.