Abstract
The fluctuation-dissipation theorem (FDT) connecting the response of the system to external perturbations with the fluctuations at thermodynamic equilibrium is a central result in statistical physics. There has been effort devoted to extending the FDT in several different directions since its original formulation. In this work we establish a generalized form of the FDT for spatially extended nonequilibrium stochastic systems described by continuous fields. The generalized FDT is formulated with the aid of the nonequilibrium force decomposition in the potential landscape and flux field theoretical framework. The general results are substantiated in the setting of the Ornstein-Uhlenbeck (OU) process and further illustrated by a more specific example worked out in detail. The key feature of this generalized FDT for nonequilibrium spatially extended systems is that it represents a ternary relation rather than a binary relation as the FDT for equilibrium systems does. In addition to the response function and the time derivative of the field-field correlation function that are present in the equilibrium FDT, the field-flux correlation function also enters the generalized FDT. This additional contribution originates from detailed balance breaking that signifies the nonequilibrium irreversible nature of the steady state. In the special case when the steady state is an equilibrium state obeying detailed balance, the field-flux correlation function vanishes and the ternary relation in the generalized FDT reduces to the binary relation in the equilibrium FDT.
Highlights
The fluctuation-dissipation theorem (FDT) is a cornerstone in equilibrium statistical physics, which establishes a connection between the response of the system to external perturbations and the correlation of fluctuations at thermodynamic equilibrium [1]
One way to understand the physical meaning of the generalized FDT is to interpret the flux correlation as a form of dissipative response associated with detailed balance breaking in non-equilibrium steady states, which contributes to how the system responds to perturbations in totality
It is a matter of perspective whether to interpret the flux correlation as part of the response function or part of the field correlation. It is the ternary relation quantified by the generalized FDT that has the final word on how the response function and the field correlation should be related to each other by the additional flux correlation when the steady state of the system is nonequilibrium in nature
Summary
The fluctuation-dissipation theorem (FDT) is a cornerstone in equilibrium statistical physics, which establishes a connection between the response of the system to external perturbations and the correlation of fluctuations at thermodynamic equilibrium [1]. Much effort has been devoted to the study of the violation of the FDT in systems out of equilibrium, for instance, in glassy systems [3], granular matter [4] and colloidal suspensions [5]. There has been growing interest in recent years to construct modified forms of the FDT beyond its original range of applications [6,7,8,9,10,11,12,13,14,15,16]. Effort has been directed to modifying the forms of the FDT around nonequilibrium steady states [10,11,12,13,14,15]. Study been carried out to generalize the FDT to non-stationary states and other directions [16].
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