Fluctuations and response in a non-equilibrium micron-sized system

Abstract

The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two correlation functions of the observable of interest: one with the entropy excess and the second with the excess of dynamical activity with respect to the unperturbed process, without recourse to anything but the dynamics of the system. We illustrate this approach in the experimental determination of the linear response of the potential energy of a Brownian particle in a toroidal optical trap. The overdamped particle motion is effectively confined to a circle, undergoing a periodic potential and driven out of equilibrium by a non-conservative force. Independent direct and indirect measurements of the linear response around a non-equilibrium steady state are performed in this simple experimental system. The same ideas are applicable to the measurement of the response of more general non-equilibrium micron-sized systems immersed in Newtonian fluids either in stationary or non-stationary states and possibly including inertial degrees of freedom.

12 pages, submitted to J. Stat. Mech., revised version

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• Frenesy: time-symmetric dynamical activity in nonequilibria
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• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• Current large deviations for driven periodic diffusions
• Response theory: a trajectory-based approach
• Potential and Flux Decomposition for Dynamical Systems and Non-Equilibrium Thermodynamics: Curvature, Gauge Field and Generalized Fluctuation-Dissipation Theorem
• Heat capacity in nonequilibrium steady states
• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• The modified Sutherland--Einstein relation for diffusive nonequilibria
• Monotone return to steady nonequilibrium
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• Solution to the Fokker-Planck equation for slowly driven Brownian motion: Emergent geometry and a formula for the corresponding thermodynamic metric
• Thermodynamic formalism and linear response theory for non-equilibrium steady states
• Energetics of critical oscillators in active bacterial baths
• Transition path time over a barrier of a colloidal particle in a viscoelastic bath
• Inducing a bound state between active particles
• Finite sampling effects on generalized fluctuation-dissipation relations for steady states