Related papers: Coarse Graining Empirical Densities and Currents i…
We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or non-equilibrium steady states on all time scales. We unravel a deep connection…
Complex physical dynamics can often be modeled as a Markov jump process between mesoscopic configurations. When jumps between mesoscopic states are mediated by thermodynamic reservoirs, the time-irreversibility of the jump process is a…
A fundamental question in nonequilibrium statistical physics is whether effective equilibrium behavior can emerge at coarse-grained scales in strongly driven systems. Here, we investigate this question in the context of human mobility by…
The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which the coarse-graining is…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through…
Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…
We investigate the evolution of the phase-space distribution function around slightly perturbed stationary states and the process of violent relaxation in the context of the dissipationless collapse of an isolated spherical self-gravitating…
We present technical results required for the description and understanding of correlations and fluctuations of the empirical density and current as well as diverse time-integrated and time-averaged thermodynamic currents of diffusion…
Characterizing current fluctuations in a steady state is of fundamental interest and has attracted considerable attention in the recent past. However, the bulk of the studies are limited to systems that either do not exhibit a phase…
We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski…
Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the system onto a smaller set of variables which captures the…
The emergence of macroscopic variables can be effected through {\it coarse graining}. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
We systematically derive an exact coarse-grained description for interacting particles with thermodynamically consistent stochastic dynamics, applicable across different observation scales, the mesoscopic and the macroscopic. We implement…
For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a…
Coarse-grained models are widely used to explain the effective behavior of partially observable physical systems with hidden degrees of freedom. Reduction procedures in state space typically disrupt Markovianity and a fluctuation relation…
Finite stochastic Markov models play a major role for modelling biochemical pathways. Such models are a coarse-grained description of the underlying microscopic dynamics and can be considered mesoscopic. The level of coarse-graining is to a…
Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe…