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Register a new userA general fluctuation-response relation for noise variations and its application to driven hydrodynamic experiments
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The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent nontrivial diffusivity matrices, as we show with an application to an experiment of two trapped and hydrodynamically coupled colloids, one of which is subject to an external random forcing that mimics an effective temperature. The nonequilibrium susceptibility of the energy to a variation of this driving is an example of our formulation, which improves an earlier version, as it does not depend on the time-discretization of the stochastic dynamics. This scheme holds for generic systems with additive noise and can be easily implemented numerically, thanks to matrix operations.
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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 terms of suitable correlation functions computed in the unperperturbed dynamics. In these relations, typically one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in non-standard cases, including driven granular media, systems with a multiscale structure, active matter and systems showing anomalous diffusion.
Here we present a model for a small system combined with an explicit entropy bath that is comparably small. The dynamics of the model is defined by a simple matrix, M. Each row of M corresponds to a macrostate of the system, e.g. net alignment, while the elements in the row represent microstates. The constant number of elements in each row ensures constant entropy, which allows reversible fluctuations, similar to information theory where a constant number of bits allows reversible computations. Many elements in M come from the microstates of the system, but many others come from the bath. Bypassing the bath states yields fluctuations that exhibit standard white noise; whereas with bath states the power spectral density varies as S(f)~1/f over a wide range of frequencies, f. Thus, the explicit entropy bath is the mechanism of 1/f noise in this model. Both forms of the model match Crooks fluctuation theorem exactly, indicating that the theorem applies not only to infinite reservoirs, but also to finite-sized baths. The model is used to analyze measurements of 1/f-like noise from a sub-micron tunnel junction.
We report on the onset of anti-resonant behaviour of mass transport systems driven by time-dependent forces. Anti-resonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an anti-resonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.
Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse-grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around equilibrium, we show that the emerging transition rates satisfy local detailed balance (LDB). Namely, the log ratio of the transition rates between nearby basins of attractions equals the free-energy variation appearing at equilibrium, supplemented by the work done by the nonconservative forces along the typical transition path. When the mesoscopic dynamics possesses a large-size deterministic limit, it can be further reduced to a jump process over macroscopic states satisfying LDB. The persistence of LDB under coarse graining of weakly nonequilibrium states is a generic consequence of the fact that only dissipative effects matter close to equilibrium.
The present work extends the well-known thermodynamic relation $C=beta ^{2}< delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $< delta beta delta {E}> =1+< delta {E^{2}}% > partial ^{2}S(E) /partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $beta (E) =partial S(E) /partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.
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