Stochastic heat engine using a single Brownian ellipsoid.

Abstract

Optical tweezers can confine position as well as orientation of a Brownian particle by simultaneously exerting restoring force and torque on it. Here we propose the theoretical model of a microscopic Stirling engine, using a Brownian ellipsoid as its working substance. The position and orientation degrees of freedom of the ellipsoid (in two dimensions), both being confined harmonically by the tweezers, are coupled to a hot and a cold thermal bath time-periodically. The stiffness of the force confinement is also time-periodic such that it resembles a pistonlike protocol, driving the Brownian ellipsoid through the strokes of a Stirling cycle. The ellipsoid takes heat from the hot bath and partially converts it into useful thermodynamic work. The extracted work and input heat shows explicit dependence on the geometry and orientation of the ellipsoid. The operational characteristics of the anisotropic Stirling engine is analyzed using the variance in work and average efficiency in the quasistatic regime. Several ways have been proposed to yield maximum efficiency at a minimum fluctuation in the output. The dissipative coupling between the position and orientation of the ellipsoid, arising due to its spherical-asymmetry and orientational bias, plays an important role in optimizing the engine characteristics. Finally, we have analytically explored the slightly anisotropic regime, where the equations of motion can be linearized. Average extracted work has been calculated in this regime, exhibiting an excellent agreement with the numerical results of the fully anisotropic system, when subjected to the stipulated range of parameters.