Related papers: Fundamental problems in Statistical Physics XIV: L…
We discuss fluctuation-dissipation relations valid under general conditions even out of equilibrium. The response function is expressed in terms of unperperturbed correlation functions, where contributions peculiar to non-equilibrium can…
In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
We study the correlation function and mean linear response function of the velocity Fourier mode of statistically steady-state, homogeneous and isotropic turbulence in the Eulerian and Lagrangian coordinates through direct numerical…
Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two…
The fluctuation-dissipation theorem is a cornerstone result in statistical mechanics that can be used to translate the statistics of the free natural variability of a system into information on its forced response to perturbations. By…
In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a…
This essay fuses concepts and approaches used to describe fluctuating phenomena in climate systems and statistical mechanics, and explores new ideas essential for understanding such phenomena. Its starting points are the Langevin equation…
The currently existing theory of fluorescence correlation spectroscopy(FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in…
In this expository note we highlight the correlation function method as a unified approach in proving both hydrodynamic limits and fluctuation limits for reaction diffusion particle systems. For simplicity we focus on the case when the…
The exponential correlation function is theoretically incorrect in the entire frequency range of interest for processes described in terms of linear response theory. The Lorentzian lineshape results from an inconsistent assumption of…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…
We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior $<x^2 > \sim t^{1/2}$. We show the validity of the usual Fluctuation-Dissipation…
We consider the modified Ising model introduced by de Oliveira et al. [J.Phys.A {\bf 26}, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a…
The force autocorrelation function (FACF), a concept of fundamental interest in statistical mechanics, encodes the effect of interactions on the dynamics of a tagged particle. In equilibrium, the FACF is believed to decay monotonically in…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables.…
The generating functional is derived for the fluctuation-dissipation relations which result from the unitarity and reversibility of microscopic dynamics and connect various statistical characteristics of many consecutive (continuous)…
For systems close to equilibrium, the relaxation properties of measurable physical quantities are described by the linear response theory and the fluctuation-dissipation theorem (FDT). Accordingly, the response or the generalized…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…