Energetics of critical oscillators in active bacterial baths

Abstract

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 scaling exponent of the average power $⟨\dot{W}⟩\sim (D_{\mathrm{a}}/\tau {)}^{1/4}$ where $D_{\mathrm{a}}$ is the effective diffusivity and $\tau$ the correlation time of the bacterial bath described by a Gaussian colored noise. Other features that we investigate are the average 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 $\tau$ that is below its zero-temperature limit. Furthermore, we reveal a finite-time uncertainty relation for active matter which leads to values of the Fano factor of the work that can be below $2k_{\mathrm{B}}{T}_{\mathrm{eff}}$, with $T_{\mathrm{eff}}$ 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 by considering the example of driven colloidal particles in periodic optical potentials within an E. Coli bacterial bath.

29 pages, 11 figures

References in corpus (16)

• Motility-Induced Phase Separation
• Thermodynamic uncertainty relation for biomolecular processes
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• Sedimentation, trapping, and rectification of dilute bacteria
• Generalized energy equipartition in harmonic oscillators driven by active baths
• Cost and Precision of Brownian Clocks
• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• Entropy production of active particles and for particles in active baths
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Directed transport of active particles over asymmetric energy barriers
• Universal Bound on the Fano Factor in Enzyme Kinetics
• Active escape dynamics: the effect of persistence on barrier crossing
• Underdamped Active Brownian Heat Engine
• Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles
• Fluctuations and response in a non-equilibrium micron-sized system
• A Volterra-series approach to stochastic nonlinear dynamics: The Duffing oscillator driven by white noise

Cited by in corpus (2)

• Nonequilibrium fluctuations of chemical reaction networks at criticality: The Schlögl model as paradigmatic case
• Excess and loss of entropy production for different levels of coarse-graining