Nonlinear Langevin functionals for a driven probe

Abstract

When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals, by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism: i) For a particle driven with prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third or second order response, respectively.

arXiv comment14 pages, 9 figures

References in corpus (40)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Anomalous transport in the crowded world of biological cells
• Fluctuations and response of nonequilibrium states
• The effective temperature
• Mode-Coupling Theory of the Glass Transition: A Primer
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Asymptotic laws for tagged-particle motion in glassy systems
• Active and Nonlinear Microrheology in Dense Colloidal Suspensions
• Frenesy: time-symmetric dynamical activity in nonequilibria
• A First-Principles Constitutive Equation for Suspension Rheology
• Oscillations of a solid sphere falling through a wormlike micellar fluid
• Coarse-Grained Modelling Out of Equilibrium
• Oscillating Modes of Driven Colloids in Overdamped Systems
• Geometry-induced superdiffusion in driven crowded systems
• Power functional theory for many-body dynamics
• A dynamic density functional theory for particles in a flowing solvent
• Response theory: a trajectory-based approach
• Dynamic density functional study of a driven colloidal particle in polymer solutions
• On the "generalized Generalized Langevin Equation"
• A meaningful expansion around detailed balance
• Nonlinear Response in the Driven Lattice Lorentz Gas
• Colloids dragged through a polymer solution: experiment, theory and simulation
• Oscillatory Motion of Rising Bubbles in Wormlike Micellar Fluids with Different Microstructures
• Frenetic aspects of second order response
• Mori-Zwanzig projection operator formalism for systems with time-dependent Hamiltonians
• Velocity gradient power functional for Brownian dynamics
• Nonlinear microrheology of dense colloidal suspensions: a mode-coupling theory
• The modified Langevin description for probes in a nonlinear medium
• On the dynamics of reaction coordinates in classical, time-dependent, many-body processes
• Properties of a nonlinear bath: Experiments, theory, and a stochastic Prandtl-Tomlinson model
• Oscillatory force autocorrelations in equilibrium odd-diffusive systems
• Flow and structure in nonequilibrium Brownian many-body systems
• Response of active Brownian particles to shear flow
• Driven probe under harmonic confinement in a colloidal bath
• Two step micro-rheological behavior in a viscoelastic fluid
• Recoil experiments determine the eigenmodes of viscoelastic fluids
• How are mobility and friction related in viscoelastic fluids?
• Memory-induced oscillations of a driven particle in a dissipative correlated medium
• The rise and fall of branching: a slowing down mechanism in relaxing wormlike micellar networks
• A Thermodynamic Non-Linear Response Relation