Stochastic Energetics of non-linear oscillators in active baths

Abstract

Active matter is systems whose individual units continuously extract energy from the environment to produce some mechanical output. Examples range from bacterial propulsion, Janus particles to flocks of birds. Non-equilibrium properties of active matter have been recently utilized to produce useful work and design systems to rectify the activity of the bath, yet little is known about the work extraction from an active medium. In this thesis, we carefully study the statistics of thermodynamic quantities of a non-linear oscillator, called Adler oscillator, kept in the presence of an active bath(Eg. bacterial bath), in particular, we compute the power and work inputted into the system. In the process, we also look at the case of a thermal bath, which occurs as the low-correlation time limit of the active bath and elaborate on the effects of correlation time. In the presence of active bath, the effect of the correlation time has been explored for the overdamped system near the bifurcation point. The main results of the thesis are : (i) In the case of a thermal bath, we exactly derive analytical expressions for the average power and variance in work at large times inputted into the system in the overdamped limit. (ii) In the underdamped limit, we found that the system has very high relaxation time to reach a unique steady state in the bistable region, and hence one can see signs of hysteresis effects in the presence of bath for long computation times O(107).(iii) Numerical studies have been done to show that uni ed colored noise approximation doesn't capture the steady-state properties, whereas Fox's approximation converges for small correlation times until there isn't signi cant deviation from Gaussian distribution in the angular velocity. (iv)Control of the activity of the bath can be used to regulate the power statistics. (v) Increased activity of the bath can be used to enhance the diffusive behavior at the bifurcation point, more than in the thermal bath case. We also found that the variance in work inputted at large times increases with the activity of the bath at the bifurcation point. (vi)Numerical studies suggest that for values above the bifurcation point, there exists a nite critical correlation time when the average power inputted into the system is minimum, that can be below the deterministic case.