Energetics of critical oscillators in active bacterial baths

We investigate the nonequilibrium energetics near a critical point of a non-linear driven oscillator immersed in an active bacterial bath. At the critical point, we reveal a novel scaling exponent of the average power in terms of the effective diffusivity and the correlation time of the bacterial bath. We also investigate the mean stationary power and the variance of the work both below and above the saddle-node bifurcation. Above the bifurcation, the average power attains an optimal, minimum value for finite correlation time that is below its zero-temperature limit. We also reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below 2k_B T_eff, with T_eff the effective temperature of the oscillator in the bacterial bath. We analyze different Markovian approximations to describe the nonequilibrium stationary state of the system. Finally, we illustrate our results in the experimental context considering driven colloidal particles in periodic optical potentials within an E. Coli bacterial bath.
[1] arXiv:2011.00858 (2020)