Stochastic resonance in periodic potentials

Saikia, Shantu; Jayannavar, A. M.; Mahato, Mangal C.

doi:10.1103/physreve.83.061121

Cited by 64 publications

(66 citation statements)

References 58 publications

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“…However, very little work has been done on SR in periodic potentials. [27][28][29] In the pendulum system, it is shown 27 that the exhibited resonant behaviour is not the SR associated with the hopping between the wells, but it is a noise enhanced resonance due to the intra-well motion. Furthermore, and due to the diffusion dynamics, there is no synchronization of the dynamical variable and the periodic driving force.…”

Section: Introductionmentioning

confidence: 97%

Novel vibrational resonance in multistable systems

Rajasekar

Abirami²,

Sanjuán³

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.

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Section: Introductionmentioning

confidence: 97%

Novel vibrational resonance in multistable systems

Rajasekar

Abirami²,

Sanjuán³

2011

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…These systems can be theoretically analyzed using stochastic thermodynamics. Exchange of energy between the particle and its surroundings becomes stochastic and yet one can clearly formulate the notion of work, heat and entropy production for a given microscopic trajectory of the particle [2,3,4,5,6,7,8,9]. Recently obtained exact results (fluctuation theorems [11,10,12,13,14,15]) put constraints on the distributions of the above mentioned stochastic quantities and are valid for systems driven far from equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Brownian refrigerator

Rana

Pal

Saha

et al. 2016

Physica A: Statistical Mechanics and its Applications

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We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the system cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on the bath temperatures. Interestingly, in non-quasistatic regime, our system can even work as a stochastic heat engine for certain range of cycle time and bath temperatures. We show that the operation of this engine is not reliable. The fluctuations of stochastic efficiency/coefficient of performance (COP) dominate their mean values. Their distributions show power law tails, however the exponents are not universal. Our study reveals that microscopic machines are not the microscopic equivalent of the macroscopic machines that we come across in our daily life. We find that there is no one to one correspondence between the performance of our system under engine protocol and its reverse.

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“…work, heat, total entropy, internal energy etc.) are defined over a single trajectory and thereby differs stochastically from one measurement to another [20,21,22,23,24,25,26,27]. Besides validating macro thermodynamics after averaging over all possible trajectories, the new frame work offers first law like equality defined over a single trajectory and fluctuation theorems [28,29,30,31,32,33], a set of equalities between stochastically varying thermodynamic variables that put rigorous constraints to their distributions.…”

Section: Introductionmentioning

confidence: 99%

Operational characteristics of single-particle heat engines and refrigerators with time-asymmetric protocol

Pal

Saha

Jayannavar

2016

Int. J. Mod. Phys. B

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We have studied the single particle heat engine and refrigerator driven by time asymmetric protocol of finite duration. Our system consists of a particle in a harmonic trap with time-periodic strength that drives the particle cyclically between two baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. The system works in irreversible mode of operation even in the quasistatic regime. This is indicated by finite entropy production even in the large cycle time limit. Consequently, Carnot efficiency for heat engine or Carnot Co-efficient of performance (COP) for refrigerators are not achievable. We further analysed the phase diagram of heat engines and refrigerators. They are sensitive to time-asymmetry of the protocol. Phase diagram shows several interesting features, often counterintuitive. The distribution of stochastic efficiency and COP is broad and exhibits power law tails.In recent years a lot of interest has been generated in the study of stochastic single particle heat engines and refrigerators [1,2,3,4,5,6,7,8,9,10,11]. Engines at nanoscale are ubiquitous in biology [12,13,14] and become increasingly pertinent synthetically. With the progress of technology micrometer sized stochastic heat engines have been realised experimentally [15,16,17,18]. At these length scales thermal fluctuation plays a pivotal role in determining the performance characteristics of the system. Typical energy transformations (work and heat) in these systems are of the order of k B T , where T is the temperature of the surrounding reservoir.Therefore taking account of thermal fluctuations is an absolute necessity to achieve engineering capabilities in designing such small scale devices [19].The apt theory for the thermodynamics of small scale devices comes under the frame work of stochastic thermodynamics where the macroscopic thermodynamic variables (e.g. work, heat, total entropy, internal energy etc.) are defined over a single trajectory and thereby differs stochastically from one measurement to another [20,21,22,23,24,25,26,27]. Besides validating macro thermodynamics after averaging over all possible trajectories, the new frame work offers first law like equality defined over a single trajectory and fluctuation theorems [28,29,30,31,32,33], a set of equalities between stochastically varying thermodynamic variables that put rigorous constraints to their distributions.Using stochastic thermodynamics microscopic heat engines and refrigerators have been explored. Extensive studies including both quasistatic and nonquasistatic regime have been done on systems consisting of a harmonically trapped Brownian particle driven periodically (with period τ ) by the time dependent strength of the confining potential within two thermal reservers having different temperatures T h and T l where T h > T l [10,11]. The protocol studied in [10,11] consists of two isotherms having equal length along time axis (that is why the protocol can be termed as time-symmetric) and two adia...

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Stochastic resonance in periodic potentials

Cited by 64 publications

References 58 publications

Novel vibrational resonance in multistable systems

Novel vibrational resonance in multistable systems

Anomalous Brownian refrigerator

Operational characteristics of single-particle heat engines and refrigerators with time-asymmetric protocol

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