Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States

Abstract

We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and non-trivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system's dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the central-limit regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods.

Version accepted for publication in Physical Review Research

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• Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space
• Perspective: Time irreversibility in systems observed at coarse resolution
• Thermodynamic bounds on generalized transport: From single-molecule to bulk observables
• Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways
• Mutual information as a measure of mixing efficiency in viscous fluids
• Brownian particles in periodic potentials: coarse-graining versus fine structure
• The Dance of Odd-Diffusive Particles: A Fourier Approach
• On correlations and fluctuations of time-averaged densities and currents with general time-dependence
• Entropy bound for time reversal markers
• Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus
• Precisely controlled colloids: A playground for path-wise non-equilibrium physics
• Force-free kinetic inference of entropy production