Analysis on the origin of directed current from a class of microscopic chaotic fluctuations

Effects of correlation in an information ratchet with finite tape

With the finite-tape autonomous information ratchet modeled by He et al. [Phys. Rev. E 105, 054131 (2022)2470-004510.1103/PhysRevE.105.054131], we recast the information processing second law, giving a tighter bound on the work extracted, in terms of the marginal bit-ratchet distribution defined from the joint tape-ratchet distribution. The marginal distribution is further utilized to probe and elucidate the conditions that lead to the presence of equilibrium and nonequilibrium stationary states in general, which are related to the effects of correlation. Applying our analysis to two designs of this information ratchet, where correlations within manifest differently, we uncover the mathematical condition for equilibrium stationary states for information ratchets that harness correlation, to identify them for engine operation during the transient phase.

Deterministic Smoluchowski-Feynman ratchets driven by chaotic noise

We have elucidated the effect of statistical asymmetry on the directed current in Smoluchowski-Feynman ratchets driven by chaotic noise. Based on the inhomogeneous Smoluchowski equation and its generalized version, we arrive at analytical expressions of the directed current that includes a source term. The source term indicates that statistical asymmetry can drive the system further away from thermodynamic equilibrium, as exemplified by the constant flashing, the state-dependent, and the tilted deterministic Smoluchowski-Feynman ratchets, with the consequence of an enhancement in the directed current.

Chaotic resonance: two-state model with chaos-induced escape over potential barrier

We consider the resonant effects of chaotic fluctuations on a strongly damped particle in a bistable potential driven by weak sinusoidal perturbation. We derive analytical expressions of chaos-induced transition rate between the neighboring potential wells based on the inhomogeneous Smoluchowski equation. Our first-order analysis reveals that the transition rate has the form of the Kramers escape rate except for a perturbed prefactor. This modification to the prefactor is found to arise from the statistical asymmetry of the chaotic noise. By means of the two-state model and the chaos-induced transition rate, we arrive at an analytical expression of the signal-to-noise ratio (SNR). Our first-order SNR shows that chaotic resonance can correspond directly to stochastic resonance.

Chaos-induced escape over a potential barrier

We investigate the statistical parity of a class of chaos-generated noises on the escape of strongly damped particles out of a potential well. We show that statistical asymmetry in the chaotic fluctuations can lead to a skewed Maxwell-Boltzmann distribution in the well. Depending on the direction of skew, the Kramers escape rate is enhanced or suppressed accordingly. Based on the Perron-Frobenious equation, we determine an analytical expression for the escape rate's prefactor that accounts for this effect. Furthermore, our perturbative analysis proves that in the zeroth-order limit, the rate of particle escape converges to the Kramers rate.