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We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…
Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the…
A generalized fluctuation-response relation is found for thermal systems driven out of equilibrium. Its derivation is independent of many details of the dynamics, which is only required to be first-order. The result gives a correction to…
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…
The role of fluctuation-dissipation relations (theorems) for the magnetization dynamics with Landau-Lifshitz-Gilbert and Bloch-Bloembergen damping terms are discussed. We demonstrate that the use of the Callen-Welton fluctuation-dissipation…
The fluctuation-response relation is a fundamental relation that is applicable to systems near equilibrium. On the other hand, when a system is driven far from equilibrium, this relation is violated in general because the detailed-balance…
In the context of an exactly soluble out of equilibrium (quenched) model, we study an extension of the fluctuation-dissipation relation. This involves a modified differential form of this relation, with an effective temperature which may…
The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the…
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 this Article we review some recent progresses in the field of non-equilibrium linear response theory. We show how a generalization of the fluctuation-dissipation theorem can be derived for Markov processes, and discuss the…
In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
The fluctuation-dissipation theory is grounded on the Langevin condition expressing the local independence between the thermal force and the particle velocity history. Upon hydrodynamic grounds, it is reasonable to relax this condition in…
The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
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 fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation. The transition rates are assumed to obey detailed balance also in the presence of a field. It is shown that in general the linear…
A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong.
We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval $t$. A heat, which differs from a work by an energy change, is shown to…
We corroborate the idea of a close connection between replica symmetry breaking and aging in the linear response function for a large class of finite-dimensional systems with short-range interactions. In these system, characterized by a…