Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics

Klages, Rainer

doi:10.1142/5945

Cited by 98 publications

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“…Research performed over the past Rainer Klages, Aleksei V. Chechkin and Peter Dieterich: Anomalous Fluctuation RelationsChap. 1 -2012/6/7 -19:43 -page 2 2 ten years has shown that FRs hold for a great variety of systems thus featuring one of the rare statistical physical principles that is valid even very far from equilibrium: see summaries in [13,14,15,16,17,18] for stochastic processes, [19,20,21,22,23,24] for deterministic dynamics and [25,26] for quantum systems. Many of these relations have meanwhile been verified in experiments on small systems, i.e., systems on molecular scales featuring only a limited number of relevant degrees of freedom [27,28,29,30,31,32], cf.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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Abstract. We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: Lévy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.

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Section: Introductionmentioning

confidence: 99%

Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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“…That is, the observed drift behavior does not appear to be consistent with a system having a positive Liapunov exponent. Random-looking evolution in time, however, may also occur under conditions that are weaker than that described by a positive Liapunov exponent, in which the separation of nearby trajectories is weaker than exponential [16], [17]. In particular, weakly chaotic systems exhibit anomalous dynamics characterized by novel properties such as ageing, which reflects a weak (power-law) relaxation towards equilibrium [17].…”

Section: Discussionmentioning

confidence: 99%

Physically-Informed Correction of Instability (Drift)

Jamasb¹

2012

IJCEE

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Abstract-A Physical model for the long-term deterministic behavior associated with instability (or drift) in pH-sensitive ion-selective field effect transistors (ISFET's) has been employed to distinguish between drift and the inherent low-frequency (1/f) noise, both of which corrupt the sensor output signal. Based on this model, a physically-informed method for sensor signal enhancement in the time-domain has been proposed, which relies on proper windowing of the sensor output. The random-like evolution in time associated with a weak power-law relaxation towards equilibrium is the key aspect of the model for drift that is utilized in the proposed corrective scheme. Drift may be interpreted as a weakly chaotic behavior, exhibiting anomalous dynamics characterized by ageing, which reflects a weak (power-law) relaxation towards equilibrium.

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“…On average, the steady state system collapses onto an attractor of lower dimension 7,11 than the ostensible phase space dimension. This dimensional collapse leads to the divergence of the Gibbs entropy to negative infinity.…”

Section: ͑24͒mentioning

confidence: 99%

“…Since the system is T-mixing, a unique steady state is generated for any given temperature gradient. If we assume that in the weak temperature gradient limit the thermal conductivity is finite ͑there are divergent systems especially in one dimension 11 where it is thought that the limiting zero gradient thermal conductivity scales with system size͒, then the limiting thermal conductivity must be positive. ͑The thermal conductivity cannot be zero since in T-mixing systems, the only state that has zero dissipation is the equilibrium state.…”

Section: ͑24͒mentioning

confidence: 99%

On the probability of violations of Fourier’s law for heat flow in small systems observed for short times

Evans

Searles

Williams

2010

The Journal of Chemical Physics

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On the probability of violations of Fourier's law for heat flow in small systems observed for short times We study the statistical mechanics of thermal conduction in a classical many-body system that is in contact with two thermal reservoirs maintained at different temperatures. The ratio of the probabilities, that when observed for a finite time, the time averaged heat flux flows in and against the direction required by Fourier's Law for heat flow, is derived from first principles. This result is obtained using the transient fluctuation theorem. We show that the argument of that theorem, namely, the dissipation function is, close to equilibrium, equal to a microscopic expression for the entropy production. We also prove that if transient time correlation functions of smooth zero mean variables decay to zero at long times, the system will relax to a unique nonequilibrium steady state, and for this state, the thermal conductivity must be positive. Our expressions are tested using nonequilibrium molecular dynamics simulations of heat flow between thermostated walls.

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Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics

Cited by 98 publications

References 0 publications

Anomalous Fluctuation Relations

Anomalous Fluctuation Relations

Physically-Informed Correction of Instability (Drift)

On the probability of violations of Fourier’s law for heat flow in small systems observed for short times

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