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 have proposed the theoretical model of a microscopic Stirling engine, using a passive Brownian ellipsoid as its working substance. The position and the orientation degrees of freedom (DoF) of the ellipsoid in two dimensions (2D), 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 piston-like protocol which drives 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 shape of the working substance as well as its orientational bias. The operational characteristics of the anisotropic Stirling engine is analyzed using the variance in work and efficiency (in the quasi-static regime), where the latter is bounded by both the Carnot limit as well as the isotropic benchmark. 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, that arises due to its spherical-asymmetry (or, shape anisotropy) and a finite mean orientation, plays an important role to optimize the engine characteristics. Finally, we have analytically explored the slightly anisotropic regime, where the coupling is linearized by suitably tuning the system parameters. The average extracted work has also been calculated in this case, which shows an excellent agreement with the numerical results of the fully anisotropic system, when subjected to the stipulated range of parameters.