Abstract
The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and sawtooth waves) with period T and amplitude A, we investigate the performance (energetics, mean current, Stokes efficiency) of a rocking ratchet in light of thermodynamic quantities (entropy production) and the path-dependent information geometric measures. For each G(t), we calculate exact time-dependent probability density functions under different conditions by varying T, A and the strength of the stochastic noise D in an unprecedentedly wide range. Overall similar behaviours are found for different cases of G(t). In particular, in all cases, the current, Stokes efficiency and the information rate normalised by A and D exhibit one or multiple local maxima and minima as A increases. However, the dependence of the current and Stokes efficiency on A can be quite different, while the behaviour of the information rate normalised by A and D tends to resemble that of the Stokes efficiency. In comparison, the irreversibility measured by a normalised entropy production is independent of A. The results indicate the utility of the information geometry as a proxy of a motor efficiency.
Highlights
Symmetry plays a key role in physics and other sciences
Unlike man-made deterministic motors where noise has a negative effect on its performance, the Brownian motor works in a noisy environment far from equilibrium in the presence of spatial asymmetry; thermal fluctuations are preferentially rectified in one direction due to the asymmetry to allow them in the favoured direction while blocking those in the opposite direction [4]
It is worth noting that this paper focuses on elucidating the path-dependent information geometry in the efficiency of the Brownian motor and comparing with some of the popular measures of irreversibility
Summary
Symmetry plays a key role in physics and other sciences. One important example is the so-called Brownian motor (e.g., [1,2,3,4,5,6]) whose function hinges on the very presence of symmetry-breaking. Unlike man-made deterministic motors where noise has a negative effect on its performance, the Brownian motor works in a noisy environment far from equilibrium in the presence of spatial asymmetry; thermal fluctuations are preferentially rectified in one direction due to the asymmetry to allow them in the favoured direction while blocking those in the opposite direction [4]. It is a useful mathematical model of molecular motors [5] of the size O (1–100) nanometres in living organisms that play a vital role in organising and orchestrating various transport processes and movement in cells. They have the capability of producing force directly rather than via an intermediate energy, by converting chemical energy, e.g., adenosine triphosphate (ATP), to kinetic energy
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