Fluctuation theorems for a non-Gaussian system

Abstract

In this work, we numerically verify the Jarzynski equality and Crook fluctuation theorem for a Brownian particle diffusing in a heterogeneous thermal bath and hence having a non-Gaussian position distribution. We use the diffusing-diffusivity model to take the account of heterogeneity of the thermal bath where the mobility is considered as a fluctuating quantity. The Brownian particle is confined by a time-dependent harmonic potential. By changing the stiffness coefficient, we perform an isothermal process. We use the stochastic thermodynamics framework to calculate the work. We find that the Jarzynski equality and the Crook fluctuation theorem are convincingly satisfied for a non-Gaussion system. We also find that the work distribution is non-Gaussian for diffusing-diffusivity system even at a larger process time.

Figures (7)

• Figure 1: The Jarzynski equality given in Eq. (\ref{['l']}) is plotted as a function of process time $\tau$. The black curve is for the Gaussian system with constant $\mu=1$. The blue, and green curves for non-Gaussian (diffusing-diffusivity) system with indicted $\sigma$, and $s$ values satisfying $\langle\mu\rangle=1$. The red solid line for theoretical value, $\langle e^{-\beta w}\rangle=1$.
• Figure 2: The probability distribution of work is plotted as a function of work, solid line is for a forward process and the dotted lineis for time-reversal processe. The black curve represents a Gaussian system with $\mu=1$. The blue, and green curves for non-Gaussian systems with indicted $\sigma$, and $s$ values and hence satisfying $\langle\mu\rangle=1$. The verticle line indicates $\langle w\rangle=0$.
• Figure 3: The fluctuation theorem given in Eq. (\ref{['b']}) is plotted for different process time $\tau$. The black curve for Gaussian system with $\mu=1$. The blue, and green curves for non-Gaussian system with indicted $\sigma$, and $s$ values with $\langle\mu\rangle=1$.
• Figure 4: The kurtosis is plotted as a function of process time $\tau$. The blue, and green curves for non-Gaussian system with indicted $\sigma$, and $s$ values with $\langle\mu\rangle=1$. The black curve for Gaussian system with $\mu=1$.
• Figure 5: The average work is plotted as a function $\tau$. The black curve for the Gaussian system with $\mu=1$. The blue, and green curves for the non-Gaussian systems with indicted $\sigma$, and $s$ values with $\langle\mu\rangle=1$.