Entropic Stochastic Resonance Research Articles

Entropic stochastic resonance of finite-size particles in confined Brownian transport.

We demonstrate the existence of entropic stochastic resonance (ESR) of passive Brownian particles with finite size in a double- or triple-circular confined cavity, and compare the similarities and differences of ESR in the double-circular cavity and triple-circular cavity. When the diffusion of Brownian particles is constrained to the double- or triple-circular cavity, the presence of irregular boundaries leads to entropic barriers. The interplay between the entropic barriers, a periodic input signal, the gravity of particles, and intrinsic thermal noise may give rise to a peak in the spectral amplification factor and therefore to the appearance of the ESR phenomenon. It is shown that ESR can occur in both a double-circular cavity and a triple-circular cavity, and by adjusting some parameters of the system, the response of the system can be optimized. The differences are that the spectral amplification factor in a triple-circular cavity is significantly larger than that in a double-circular cavity, and compared with the ESR in a double-circular cavity, the ESR effect in a triple-circular cavity occurs within a wider range of external force parameters. In addition, the strength of ESR also depends on the particle radius, and smaller particles can induce more obvious ESR, indicating that the size effect cannot be safely neglected. The ESR phenomenon usually occurs in small-scale systems where confinement and noise play an important role. Therefore, the mechanism that is found could be used to manipulate and control nanodevices and biomolecules.

Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance.

We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.

Entropic vibrational resonance and entropic stochastic resonance for a confined system with Sine-Wiener bounded noise and constant force

Entropic vibrational resonance and entropic stochastic resonance for a confined system with Sine-Wiener bounded noise and constant force

Entropic stochastic resonance of a fractional confined system driven by bounded noise

Entropic stochastic resonance of a fractional confined system driven by bounded noise

Entropic stochastic resonance for a confined system driven by two constant forces and multiplicative noise

The entropic stochastic resonance (ESR) phenomenon for a confined system driven by two constant forces, by two periodic forces and multiplicative noise is studied. The Fokker-Planck equation corresponding to the confined structure is obtianed applying Fick-Jacob approximation. The transition rates from the stable states are derived under the adiabatic approximation condition. The signal-to-noise ratios (SNRs) for the fundamental and higher harmonics are derived by virtue of two-state theory. Analysis result indicates that the SNR for fundamental harmonic decreases as increasing the constant force along x-direction, while the SNR for fundamental harmonic can obtain one maxmimum value with the increment of the constant force along y-direction. Each of the SNRs for higher harmonics can get one resonance peak as increasing the two constant forces. Two peaks appear when the SNRs vary with the multiplicative noise intensity, while only one peak value takes place when the SNRs change with the additive noise strength. The influence of the boundary parameters of the confined system on the SNRs is discussed.

Entropic stochastic resonance and super-harmonic stochastic resonance in a dichotomous fluctuating potential

When a Brownian particle moves in a confined space, the boundaries of the confined space can form an entropic barrier and thus induce the classical entropic stochastic resonance (ESR) phenomenon. This paper introduces a dichotomous fluctuating potential into the classical ESR model and studies the dynamics and ESR phenomena of the confined particle. It is shown that the amplitude of each harmonic component of both the horizontal and vertical displacements of the confined particle appears in various types of ESR phenomena, such as single-peak ESR, double-peak ESR, or even multi-peak ESR. This multi-peak ESR phenomenon is caused when the different dynamical states of the confined particle (under the joint action of the energy and entropy potentials) reach the optimal equilibrium. The results of this paper will help to understand the mechanism of stochastic dynamics of particles in confined spaces.

Phenomenon of double entropic stochastic resonance with recycled noise

The double entropic stochastic resonance (DSR) phenomenon for a Brown particle moving in a confined geometry driven by a time-dependent force in the declining direction subject to additive master noise and recycled noise is investigated in this paper. Under the adiabatic approximation condition, based on two-state theory and linear response theory, the expression for the system linear response (LR) is derived. Stochastic resonance (SR) and periodic SR behavior is observed when the LR changes with the feedback coefficient and with the time-delay of the recycled noise. DSR phenomenon appears when the LR varies with the constant component and with the fluctuation noise intensity of the force in the declining direction. Tradition SR occurs on the curve of the LR when the LR varies with the intensity of the master noise. The non-monotonous effect of the parameters of the confined structure on the LR is discussed.

Entropic stochastic resonance induced by a transverse driving force.

The phenomenon of entropic stochastic resonance (ESR) is investigated with the presence of a time-periodic force in the transverse direction. Simulation results manifest that the ESR can survive even if there is no static bias force in any direction, just if a transverse driving field is applied. In the weak noise region, the transverse driving force leads to a giant-suppression of the escape rate from one well to another, i.e. the entropic trapping. The increase in noise intensity will eliminate this suppression and induce the ESR phenomenon. An alternative quantity, called the mean free flying time, is also proposed to characterize the ESR as well as the conventional spectral power amplification. The ESR can be modulated conveniently by the transverse periodic force, which implies an alternative method for controlling the dynamics of small-scale systems. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Effects of self-propulsion, chirality and noise-correlation on the entropic stochastic resonance of an active Brownian particle

Entropic stochastic resonance (ESR) of an active Brownian particle (ABP) confined in two kinds of 2D cavities is investigated. The chirality and self-propulsion, which represent two vital characteristic features of the ABP, can enhance and suppress the ESR monotonously. Novelty, in the absence of the translational noises, the ESR can be induced by the rotational noise solely on condition that the rotational frequency is large enough. Moreover, the ESR can be detected more easily with increasing noise-correlation. This research is expected to provide a theoretical basis for controlling the ABP in confined spaces.

Entropic stochastic resonance in a confined asymmetrical bistable system with non-Gaussian noise

Particles moving in confined regions with bistable potential driven by weak signal and fluctuations may present a similar stochastic resonance (SR). This similar SR is called entropic stochastic resonance (ESR). The phenomenon of ESR in a confined asymmetrical bistable potential driven by a transverse periodic force is investigated when a non-Gaussian fluctuation is considered in the system. The left potential of the bistable system can be adjusted by introducing the asymmetrical ratio α. By the functional analysis and two-state theory, the approximate Signal-to-Noise ratio (SNR) is derived. It is found that there is a global maximum in the SNR curves when the asymmetrical ratio α and the noise intensity D are changed. It is also shown that the noise correlation time τ will suppress the ESR of the system and the departure q can obviously change the position of peak in the SNR. The above clues are helpful in achieving weak signal detection under irregular, small-scale systems.

Entropic stochastic resonance of a self-propelled Janus particle

Entropic stochastic resonance is investigated when a self-propelled Janus particle moves in a double-cavity container. Numerical simulation results indicate the entropic stochastic resonance can survive even if there is no symmetry breaking in any direction. This is the essential distinction between the property of a self-propelled Janus particle and that of a passive Brownian particle, for the symmetry breaking is necessary for the entropic stochastic resonance of a passive Brownian particle. With the rotational noise intensity growing at small fixed noise intensity of translational motion, the signal power amplification increases monotonically towards saturation which also can be regarded as a kind of stochastic resonance effect. Besides, the increase in the natural frequency of the periodic driving depresses the degree of the stochastic resonance, whereas the rise in its amplitude enhances and then suppresses the behavior.

Entropic stochastic resonance without external force in oscillatory confined space.

We have studied the dynamics of Brownian particles in a confined geometry of dumbbell-shape with periodically oscillating walls. Entropic stochastic resonance (ESR) behavior, characterizing by a maximum value of the coherent factor Q at some optimal level of noise, is observed even without external periodic force in the horizontal direction, which is necessary for conventional ESR where the wall is static and the particle is subjected to the force. Interestingly, the ESR can be remarkably enhanced by the particle gravity G, in contrast to the conventional case. In addition, Q decreases (increases) with G in the small (large) noise limit, respectively, while it non-monotonically changes with G for moderate noise levels. We have applied an effective 1D coarsening description to illustrate such a nontrivial dependence on G, by investigating the property of the 1D effective potential of entropic nature and paying special attention to the excess part resulting from the boundary oscillation. Dependences of the ESR strength with other related parameters are also discussed.

A new model of geometry-induced stochastic resonance

We propose a new model where entropic stochastic resonance and geometric stochastic resonance can both be observed by controlling the geometry parameters and the external force. Such stochastic resonance manifests a more adjustable character in small-scale systems where confinement and noise play a prominent role. The magnitude of the effect is sensitive to the geometry modification, thus leading to various resonance conditions. The novel phenomenon found could thus be beneficial for the control of the basic properties in these systems.

Application Research on Entropic Stochastic Resonance for Bearing Fault Diagnosis

The Entropic stochastic resonance (ESR) is the appearance of stochastic resonance (SR) when the dynamics of aBrownian particle takes place in a confined medium. The presence of unevenboundaries, giving rise to anentropic contribution to the potential, may upon application of a periodic driving force result in anincrease of thespectral amplification at an optimum value of the ambient noise level.The ESR provides a way for weak signal detection, and this paper applies it to bearing fault diagnosis. Preliminary numerical simulation andexperimental result of practical bearing test signal show that the ESRhas a good effect on weak feature extraction and bearing fault detection.

How a single stretched polymer responds coherently to a minute oscillation in fluctuating environments: An entropic stochastic resonance

Within the cell, biopolymers are often situated in constrained, fluid environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is of paramount importance to understand quantitatively how they, utilizing their flexibility, optimally respond to a minute signal, which is, in general, temporally fluctuating far away from equilibrium. To this end, we analytically study viscoelastic response and associated stochastic resonance in a stretched single semi-flexible chain to an oscillatory force or electric field. Including hydrodynamic interactions between chain segments, we evaluate dynamics of the polymer extension in coherent response to the force or field. We find power amplification factor of the response at a noise-strength (temperature) can attain the maximum that grows as the chain length increases, indicative of an entropic stochastic resonance (ESR). In particular for a charged chain under an electric field, we find that the maximum also occurs at an optimal chain length, a new feature of ESR. The hydrodynamic interaction is found to enhance the power amplification, representing unique polymer cooperativity which the fluid background imparts despite its overdamping nature. For the slow oscillatory force, the resonance behavior is explained by the chain undulation of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer self-organizes in an overdamping environment, utilizing its flexibility and thermal fluctuations.

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance (ESR) in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction, is investigated. Under the adiabatic approximation condition and based on the two-state theory, the expression of the output signal-to-noise ratio (SNR) is obtained. The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise, white noise, and correlated strength of correlated noise. In addition, the SNR varies non-monotonically with the increase of the shape parameters of the confined structure, and also with the increase of the constant force along the y axis of the structure. The influence of the correlation rate of the dichotomous noise, and that of the frequency of the periodic force on the SNR are discussed.

Entropic stochastic resonance of a flexible polymer chain in a confined system

We have studied the dynamics of a flexible polymer chain in constrained dumb-bell-shape geometry subject to a periodic force and external noise along the longitudinal direction. It is found that the system exhibits a feature of entropic stochastic resonance (ESR), i.e., the temporal coherence of the polymer motion can reach a maximum level for an optimal noise intensity. We demonstrate that the occurrence of ESR is robust to the change of chain length, while the bottleneck width should be properly chosen. A gravity force in the vertical direction is not necessary for the ESR here, however, the elastic coupling between polymer beads is crucial.

Entropic noises-induced resonance in a geometrically confined system

We consider the motion of Brownian particles through a narrow tube of varying cross-section in a geometrically confined system subjected to a sinusoidal oscillating force. The varying cross-section of the confinement results in an effective purely entropic potential in reduced dimension. Besides an additive Langevin force, one external additive and another multiplicative noise are acting along the x-direction. We demonstrate that the presence of a periodic input may give rise to a maximum and a minimum of the spectral amplification at corresponding optimal values of the noise strength, and therefore to the appearance of the purely entropic stochastic resonance and reverse-resonance phenomena. Furthermore, we show that the cross-correlation between two noises leads to a decrease of the spectral amplification, i.e., we observe the cross-correlation between two noises weakening the resonance. Mechanisms for the cross-correlation weakening the resonance are explained from the point of view of the effective purely entropic potential.

Phenomenon of entropic stochastic resonance with asymmetric dichotomous noise and white noise

The entropic stochastic resonance (ESR) in a confined system subject to asymmetric dichotomous noise, white noise, and a periodic square-wave signal is investigated. Under the adiabatic approximation condition, by use of the properties of the dichotomous noise, we obtain the expression of the output signal-to-noise ratio (SNR) based on two-state theory. The SNR is shown to be a nonmonotonic function of the strength and asymmetry of the dichotomous noise, the intensity of the white noise, and the amplitude of the square-wave signal. The SNR varies non-monotonically with increases in the parameters of the confined structure. The influence of the correlation rate of the dichotomous noise and the frequency of the external constant force on the SNR is also discussed.

Entropic Resonant Activation and Stochastic Resonance Driven by Non-Gaussian Noise

The transition rate and stochastic resonance (SR) of a Brownian particle moving in a confined system under the presence of entropic barriers are investigated when the system is driven by non-Gaussian noise. The explicit expressions of the transition rate and the spectral power amplification (SPA) are obtained, respectively. The effects of the parameter q indicating the departure from the Gaussian noise and the correlation time τ of the non-Gaussian noise on the transition rate and the SPA are discussed. Research results show that: (i) The transition rate as a function of the noise strength exhibits a maximum. This maximum for transition rate identifies the phenomenon of entropic resonant activation (ERA), the parameter q and the noise correlation time τ weaken the ERA of the system; (ii) The curves of SPA appear a transition from one peak to double-peak, and then to one peak again as the noise correlation time τ of non-Gaussian noise increases.