The fluctuation-dissipation relation holds for a macroscopic tracer in an active bath
Abstract: The fluctuation-dissipation relation (FDR) links thermal fluctuations and dissipation at thermal equilibrium through temperature. Extending it beyond equilibrium conditions in pursuit of broadening thermodynamics is often feasible, albeit with system-dependent specific conditions. We demonstrate experimentally that a generalized FDR holds for a harmonically trapped tracer colliding with self-propelled walkers. The generalized FDR remains valid across a large spectrum of active fluctuation frequencies, extending from underdamped to critically damped dynamics, which we attribute to a single primary channel for energy input and dissipation in our system.
- A. Einstein, On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat, Ann. Phys. (Leipzig) 17, 208 (1905).
- R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys. 29, 255 (1966).
- R. Kubo, Brownian motion and nonequilibrium statistical mechanics, Science 233, 330 (1986).
- P. Martin, A. Hudspeth, and F. Jülicher, Comparison of a hair bundle’s spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process, Proc. Natl. Acad. Sci. 98, 14380 (2001).
- J. Prost, J.-F. Joanny, and J. M. Parrondo, Generalized fluctuation-dissipation theorem for steady-state systems, Phys. Rev. Lett. 103, 090601 (2009).
- B. Dybiec, J. M. Parrondo, and E. Gudowska-Nowak, Fluctuation-dissipation relations under Lévy noises, Europhys. Lett. 98, 50006 (2012).
- B. Lindner, Fluctuation-dissipation relations for spiking neurons, Phys. Rev. Lett. 129, 198101 (2022).
- V. Lucarini and M. Colangeli, Beyond the linear fluctuation-dissipation theorem: the role of causality, J. Stat. Mech. 2012, P05013 (2012).
- D. Villamaina, A. Puglisi, and A. Vulpiani, The fluctuation-dissipation relation in sub-diffusive systems: the case of granular single-file diffusion, J. Stat. Mech. 2008, L10001 (2008).
- G. Szamel, Self-propelled particle in an external potential: Existence of an effective temperature, Phys. Rev. E 90, 012111 (2014).
- E. Flenner and G. Szamel, Active matter: Quantifying the departure from equilibrium, Phys. Rev. E 102, 022607 (2020).
- A. Solon and J. M. Horowitz, On the Einstein relation between mobility and diffusion coefficient in an active bath, J. Phys. A 55, 184002 (2022).
- G. E. Uhlenbeck and L. S. Ornstein, On the theory of the Brownian motion, Phys. Rev. 36, 823 (1930).
- V. Démery and É. Fodor, Driven probe under harmonic confinement in a colloidal bath, J. Stat. Mech. 2019, 033202 (2019).
- J. Shea, G. Jung, and F. Schmid, Passive probe particle in an active bath: can we tell it is out of equilibrium?, Soft Matter 18, 6965 (2022).
- X.-L. Wu and A. Libchaber, Particle diffusion in a quasi-two-dimensional bacterial bath, Phys. Rev. Lett. 84, 3017 (2000).
- L. Angelani, R. Di Leonardo, and G. Ruocco, Self-starting micromotors in a bacterial bath, Phys. Rev. Lett. 102, 048104 (2009).
- T. Pöschel and S. Luding, Granular gases (Springer Science & Business Media, 2001).
- J. Van Zon and F. MacKintosh, Velocity distributions in dissipative granular gases, Phys. Rev. Lett. 93, 038001 (2004).
- A. Puglisi, A. Baldassarri, and V. Loreto, Fluctuation-dissipation relations in driven granular gases, Phys. Rev. E 66, 061305 (2002).
- Y. Shokef and D. Levine, Exactly solvable model for driven dissipative systems, Phys. Rev. Lett. 93, 240601 (2004).
- Y. Shokef and D. Levine, Energy distribution and effective temperatures in a driven dissipative model, Phys. Rev. E 74, 051111 (2006).
- G. Bunin, Y. Shokef, and D. Levine, Frequency-dependent fluctuation-dissipation relations in granular gases, Phys. Rev. E 77, 051301 (2008).
- O. Dauchot and V. Démery, Dynamics of a self-propelled particle in a harmonic trap, Phys. Rev. Lett. 122, 068002 (2019).
- The mean free time between collisions τcsubscript𝜏𝑐\tau_{c}italic_τ start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT was estimated by tracking both the bbots and the tracer, averaging over the times in which there’s no physical contact between the bots and the tracer.
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