Work fluctuations and stochastic resonance

Abstract

We study Brownian particle motion in a double-well potential driven by an ac force. This system exhibits the phenomenon of stochastic resonance. Distribution of work done on the system over a drive period in the time asymptotic regime has been calculated. We show that fluctuations in the input energy or work done dominate the mean value. The mean value of work done over a period as a function of noise strength can also be used to characterize stochastic resonance in the system. We also discuss the validity of steady state fluctuation theorems in this particular system.

Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

“…For higher values of temperature, D = 0.25 (and beyond), the peak structures merge and P (∆s tot,p ) becomes closer to a Gaussian distribution. Similar observations have been made for distributions of work and heat in earlier literature [47,48]. The observed values of e −∆stot,p , from our simulations, are equal to 1.045, 1.017, 0.980, 1.024 and 1.032, for values of temperatures D = 0.06, 0.08, 0.12, 0.2 and 0.25, respectively.…”

“…However, ∆s rv shows a minimum around the same temperature at which ∆s tot,p shows a peak. Thus, unlike W rv [30,47,48], ∆s rv cannot be used as a quantifier of SR. This is because the minimum in ∆s rv is correlated to the peak in ∆s tot as a function of D, which itself does not occur at the value of the D at which resonance condition is satisfied, as discussed earlier.…”

“…The work injected into the system (or the thermodynamic work done on the system) per cycle characterizes SR as a bona fide resonance [40,45,46]. Recently work and heat fluctuation theorems have been analyzed in a symmetric double well system exhibiting SR in presence of external subthreshold harmonic [47,48] and biharmonic [49] drives. Theoretical [47,48] and experimental [28,29] studies reveal the validity of the steady state fluctuation theorem (SSFT) for heat and work integrated over finite time intervals.…”

“…Recently work and heat fluctuation theorems have been analyzed in a symmetric double well system exhibiting SR in presence of external subthreshold harmonic [47,48] and biharmonic [49] drives. Theoretical [47,48] and experimental [28,29] studies reveal the validity of the steady state fluctuation theorem (SSFT) for heat and work integrated over finite time intervals. In the following, we extend the study to fluctuation theorems for total entropy production and associated probability density functions.…”

Energy fluctuations in a biharmonically driven nonlinear system

“…To characterize this resonance phenomenon, several different quantifiers have been introduced in the literature [28,29,30,31,32,33,34,35]. One of the quantifiers, namely the input energy of the system or the work done on the system per cycle is known to characterize SR as a bona fide resonance [24,25,34,35]. In this case, the resonance can be shown to occur both as a function of noise strength and driving frequency.…”