The fluctuation-dissipation relation: how does one compare correlation functions and responses?
arXiv:0907.2791 · doi:10.1088/1742-5468/2009/07/P07024
Abstract
We discuss the well known Einstein and the Kubo Fluctuation Dissipation Relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A multi-variate linear Langevin model, which includes dynamics with memory, is used as a treatable example to show how the usual relations are recovered only in particular cases. This study brings to the fore the ambiguities of a check of the FDR done without knowing the significant degrees of freedom and their coupling. An analogous scenario emerges in the dynamics of diluted shaken granular media. There, the correlation between position and velocity of particles, due to spatial inhomogeneities, induces violation of usual FDRs. The search for the appropriate correlation function which could restore the FDR, can be more insightful than a definition of ``non-equilibrium'' or ``effective temperatures''.
22 pages, 9 figures
References in corpus (22)
- A nonequilibrium equality for free energy differences
- Dynamical ensembles in stationary states
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
- Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
- Clustering and Non-Gaussian Behavior in Granular Matter
- Shearing a Glassy Material: Numerical Tests of Nonequilibrium Mode-Coupling Approaches and Experimental Proposals
- Fluctuation-dissipation ratio of a spin glass in the aging regime
- Randomly Driven Granular Fluids: large scale structure
- Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
- Randomly Driven Granular Fluids: collisional statistics and short scale structure
- Violation of the Fluctuation Dissipation Theorem in Finite Dimensional Spin Glasses
- A kinetic approach to granular gases
- Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
- Fluctuation-Dissipation relations in Driven Granular Gases
- Violation of the Einstein relation in Granular Fluids: the role of correlations
- Temperature probes in binary granular gases
- Fluctuation-Dissipation relation in sub-diffusive systems: the case of granular single-file
- Generalized fluctuation-dissipation relation and effective temperature in off-equilibrium colloids
- Frequency-dependent fluctuation-dissipation relations in granular gases
- A scenario for the dynamics in the small intropy production limit
- Effective temperature and compactivity of a lattice-gas under gravity
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