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The spontaneously oscillating hair bundle of sensory cells in the inner earis an example of a stochastic, nonlinear oscillator driven by internal activeprocesses. Moreover, this internal activity is adaptive -- its power inputdepends on the current state of the system. We study fluctuation dissipationrelations in such adaptively-driven, nonequilibrium limit-cycle oscillators. Weobserve the expected violation of the well-known, equilibriumfluctuation-dissipation theorem (FDT), and verify the existence of ageneralized fluctuation-dissipation theorem (GFDT) in the non-adaptively drivenmodel of the hair cell oscillator. This generalized fluctuation theoremrequires the system to be analyzed in the co-moving frame associated with themean limit cycle of the stochastic oscillator. We then demonstrate, vianumerical simulations and analytic calculations, that the adaptively-drivendynamical hair cell model violates both the FDT and the GFDT. We go on to show,using stochastic, finite-state, dynamical models, that such afeedback-controlled drive in stochastic limit cycle oscillators genericallyviolates both the FDT and GFDT. We propose that one may in fact use thebreakdown of the GFDT as a tool to more broadly look for and quantify theeffect of adaptive, feedback mechanisms associated with driven (nonequilibrium)biological dynamics.

Violation of generalized fluctuation theorems in adaptively driven steady states: Applications to hair cell oscillations