Efficiency of transport in periodic potentials: dichotomous noise contra deterministic force

Abstract

We study transport of an inertial Brownian particle moving in a symmetric and periodic one-dimensional potential, and subjected to both a symmetric, unbiased external harmonic force as well as biased dichotomic noise $\eta (t)$ also known as a random telegraph signal or a two state continuous-time Markov process. In doing so, we concentrate on the previously reported regime [J. Spiechowicz et al., Phys. Rev. E 90, 032104 (2014)] for which non-negative biased noise $\eta (t)$ in the form of generalized white Poissonian noise can induce anomalous transport processes similar to those generated by a deterministic constant force $F=⟨\eta (t)⟩$ but significantly more effective than $F$, i.e. the particle moves much faster, the velocity fluctuations are noticeable reduced and the transport efficiency is enhanced several times. Here, we confirm this result for the case of dichotomous fluctuations which in contrast to white Poissonian noise can assume positive as well as negative values and examine the role of thermal noise in the observed phenomenon. We focus our attention on the impact of bidirectionality of dichotomous fluctuations and reveal that the effect of non-equilibrium noise enhanced efficiency is still detectable. This result may explain transport phenomena occurring in strongly fluctuating environments of both a physical and biological origin. Our predictions can be corroborated experimentally by use of a set-up that consists of a resistively and capacitively shunted Josephson junction.

15 pages, 6 figures

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• Time-dependent probability density functions and information geometry in stochastic logistic and Gompertz models
• Effective temperatures for single particle system under dichotomous noise
• Resonant current in coupled inertial Brownian particles with delayed-feedback control