Coarse-grained second-order response theory

@article{Muller2020CoarsegrainedSR,
  title={Coarse-grained second-order response theory},
  author={Fenna Muller and Urna Basu and Peter Sollich and Matthias Kruger},
  journal={arXiv: Statistical Mechanics},
  year={2020}
}
While linear response theory, manifested by the fluctuation dissipation theorem, can be applied on any length scale, nonlinear response theory is fundamentally of microscopic nature. We develop an exact theoretical framework for analyzing nonlinear (second order) response of coarse grained observables to time-dependent perturbations, using a path-integral formalism. The resulting expressions involve correlations of the observable with coarse grained path weights. The time symmetric part of… 

Figures and Tables from this paper

Adiabatic Approximation of Coarse Grained Second Order Response
We propose estimators for dynamic second order response theory in coarse grained variables for driven out-of-equilibrium subsystems. The error is controlled through the the notion of subsystem
Toolbox for quantifying memory in dynamics along reaction coordinates
TLDR
A set of complementary methods for quantifying conclusively the magnitude and duration of memory in a time series of a reaction coordinate is proposed.

References

SHOWING 1-10 OF 44 REFERENCES
Beyond the linear fluctuation-dissipation theorem: the role of causality
In this paper we tackle the traditional problem of relating the fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also
Extrapolation to Nonequilibrium from Coarse-Grained Response Theory.
TLDR
From the microscopic starting point, an extrapolation scheme uses near-equilibrium measurements to predict far-from-Equilibrium properties (here, second order responses) and because it does not involve system details, it can be applied to many-body systems.
Fluctuation relations and coarse-graining
We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low resolution
Nonlinear susceptibilities and the measurement of a cooperative length
We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which
Nonlinear response theory for Markov processes: simple models for glassy relaxation.
  • G. Diezemann
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the
Thermodynamic inference based on coarse-grained data or noisy measurements.
TLDR
Improved estimators of free-energy differences based on fluctuation theorems are proposed and it is shown that effective temperature appears less useful for non-Gaussian work distributions or when the error is correlated with the work, but nevertheless, improved estimators can still be constructed for such cases.
Nonlinear susceptibility in glassy systems: A probe for cooperative dynamical length scales
We argue that for generic systems close to a critical point, an extended fluctuation-dissipation relation connects the low frequency nonlinear cubic susceptibility to the four-point correlation
A meaningful expansion around detailed balance
We consider Markovian dynamics modelling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary
Fluctuating soft-sphere approach to coarse-graining of polymer models
We introduce a coarse-grained model for the simulation of the statistical properties of polymeric systems where collections of chain segments are represented by connected soft spheres of fluctuating
Frenetic aspects of second order response.
TLDR
The way in which a system's dynamical activity changes by perturbation is visible (only) from the nonlinear response.
...
...