Anomalous fluctuation properties.

We complement and extend our work on fluctuations arising in nonequilibrium systems in steady states driven by Lévy noise [H. Touchette and E. G. D. Cohen, Phys. Rev. E 76, 020101(R) (2007)]. As a concrete example, we consider a particle subjected to a drag force and a Lévy white noise with tail index mu epsilon (0,2), and calculate the probability distribution of the work done on the particle by the drag force, as well as the probability distribution of the work dissipated by the dragged particle in a nonequilibrium steady state. For 0

Fluctuation relation for a Lévy particle.

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the Lévy type. In the stationary regime, the probability density of the work is found to have "fat" power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a nonmonotonic way. Possible experiments that could probe these features are proposed.

Generalized canonical ensembles and ensemble equivalence.

This paper is a companion piece to our previous work [J. Stat. Phys. 119, 1283 (2005)], which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor of the canonical ensemble with an exponential factor involving a continuous function of the Hamiltonian . We provide here a simplified introduction to our previous work, focusing now on a number of physical rather than mathematical aspects of the generalized canonical ensemble. The main result discussed is that, for suitable choices of , the generalized canonical ensemble reproduces, in the thermodynamic limit, all the microcanonical equilibrium properties of the many-body system represented by even if this system has a nonconcave microcanonical entropy function. This is something that in general the standard canonical ensemble cannot achieve. Thus a virtue of the generalized canonical ensemble is that it can often be made equivalent to the microcanonical ensemble in cases in which the canonical ensemble cannot. The case of quadratic functions is discussed in detail; it leads to the so-called Gaussian ensemble.

Information capacity and pattern formation in a tent map network featuring statistical periodicity.

We provide quantitative support to the observation that lattices of coupled maps are "efficient" information coding devices. It has been suggested recently that lattices of coupled maps may provide a model of information coding in the nervous system because of their ability to create structured and stimulus-dependent activity patterns which have the potential to be used for storing information. In this paper, we give an upper bound to the effective number of patterns that can be used to store information in the lattice by evaluating numerically its information capacity or information rate as a function of the coupling strength between the maps. We also estimate the time taken by the lattice to establish a limiting activity pattern.

Information-theoretic limits of control

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of control systems shows feedback control to be a zero sum game: each bit of information gathered from a dynamical system by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information. Consequences for the control of discrete state systems and chaotic maps are discussed.