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It is well known that particles can get trapped by randomly placed obstacles when they are pushed too much. We present a model where the current in a disordered medium dies at a large external field, but is reborn when the activity is increased. By activity we mean the time-variation of the external driving at a constant time-averaged field. A different interpretation of the resurgence of the current is that the particles are capable of taking an infinite sequence of potential barriers via a mechanism similar to stochastic resonance. We add a discussion regarding the role of "shaking" in processes of relaxation., Comment: 13 pages, 12 figures

Strong interaction with other particles or feedback from the medium on a Brownian particle entail memory effects in the effective dynamics. We discuss the extension of the fluctuation-dissipation theorem to nonequilibrium Langevin systems with memory. An important application is to the extension of the Sutherland-Einstein relation between diffusion and mobility. Nonequilibrium corrections include the time-correlation between the dynamical activity and the velocity of the particle, which in turn leads to information about the correlations between the driving force and the particle's displacement.

The control of chemical dynamics requires understanding the effect of time-dependent transition rates between states of chemo-mechanical molecular configurations. Pumping refers to generating a net current, e.g. per period in the time-dependence, through a cycle of consecutive states. The working of artificial machines or synthesized molecular motors depends on it. In this paper we give short and simple proofs of no-go theorems, some of which appeared before but here with essential extensions to non-Markovian dynamics, including the study of the diffusion limit. It allows to exclude certain protocols in the working of chemical motors where only the depth of the energy well is changed in time and not the barrier height between pairs of states. We also show how pre-existing steady state currents are in general modified with a multiplicative factor when this time-dependence is turned on., Comment: 8 pages; v2: minor changes, 1 reference added

We analyze the exact meaning of expressions for nonequilibrium stationary distributions in terms of entropy changes. They were originally introduced by McLennan for mechanical systems close to equilibrium and more recent work by Komatsu and Nakagawa has shown their intimate relation to the transient fluctuation symmetry. Here we derive these distributions for jump and diffusion Markov processes and we clarify the order of the limits that take the system both to its stationary regime and to the close-to-equilibrium regime. In particular, we prove that it is exactly the (finite) transient component of the irreversible part of the entropy flux that corrects the Boltzmann distribution to first order in the driving. We add further connections with the notion of local equilibrium, with the Green-Kubo relation and with a generalized expression for the stationary distribution in terms of a reference equilibrium process., Comment: 22 pages

We continue the study of the free energy of quantum lattice spin systems where to the local Hamiltonian $H$ an arbitrary mean field term is added, a polynomial function of the arithmetic mean of some local observables $X$ and $Y$ that do not necessarily commute. By slightly extending a recent paper by Hiai, Mosonyi, Ohno and Petz [9], we prove in general that the free energy is given by a variational principle over the range of the operators $X$ and $Y$. As in [9], the result is a noncommutative extension of the Laplace-Varadhan asymptotic formula., Comment: v1-->v2, 15 pages, the conditions of the theorems have been relaxed and their proof has been simplified. The whole paper was therefore restyled. A new author is added

A model of the Lu-Hamilton kind is applied to the study of critical behavior of the magnetized solar atmosphere. The main novelty is that its driving is done via sources undergoing a diffusion. This mimics the effect of a virtual turbulent substrate forcing the system. The system exhibits power-law statistics not only in the size of the flares, but also in the distribution of the waiting times., Comment: 5 pages + 9 figures, Accepted to Physica A

The propagation of compressional MHD waves is studied for an externally driven system. It is assumed that the combined action of the external sources and sinks of the entropy results in the harmonic oscillation of the entropy (and temperature) in the system. It is found that with the appropriate resonant conditions fast and slow waves get amplified due to the phenomenon of parametric resonance. Besides, it is shown that the considered waves are mutually coupled as a consequence of the nonequilibrium state of the background medium. The coupling is strongest when the plasma $\beta \approx 1$. The proposed formalism is sufficiently general and can be applied for many dynamical systems, both under terrestrial and astrophysical conditions., Comment: 14 pages, 4 figures, Accepted to Physical Review E

We give a pedagogical introduction to a selection of recently discussed topics in nonequilibrium statistical mechanics, concentrating mostly on formal structures and on general principles. Part I contains an overview of the formalism of lattice gases that we use to explain various symmetries and inequalities generally valid for nonequilibrium systems, including the fluctuation symmetry, Jarzynski equality, and the direction of currents. In Part II we concentrate on the macroscopic state and how entropy provides a bridge between microscopic dynamics and macroscopic irreversibility; included is a construction of quantum macroscopic states and a result on the equivalence of ensembles., Comment: Lecture notes from the 5th Prague Summer School on Mathematical Statistical Mechanics (2006), 55 pages

The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical distribution of occupation times for a class of Markov processes, we identify the entropy production as the large deviation rate function, up to leading order when expanding around a detailed balance dynamics. In that way, the minimum entropy production principle is recognized as a consequence of the structure of dynamical fluctuations, and its approximate character gets an explanation. We also discuss the subtlety emerging when applying the principle to systems whose degrees of freedom change sign under kinematical time-reversal., Comment: 17 pages

Various notions of fluctuations exist depending on the way one chooses to measure them. We discuss two extreme cases (continuous measurement versus long inter-measurement times) and we see their relation with entropy production and with escape rates. A simple explanation of why the relative entropy satisfies a Hamilton-Jacobi equation is added., Comment: 10 pages

We study the threshold conditions of spatial self organization combined with collective coherent optical backscattering of a thermal gaseous beam moving in a high Q ring cavity with counter propagating pump. We restrict ourselves to the limit of large detuning between the particles optical resonances and the light field, where spontaneous emission is negligible and the particles can be treated as polarizable point masses. Using a linear stability analysis in the accelerated rest frame of the particles we derive an analytic bounds for the selforganization as a function of particle number,average velocity, temperature and resonator parameters. We check our results by a numerical iteration procedure as well as by direct simulations of the N-particle dynamics. Due to momentum conservation the backscattered intensity determines the average force on the cloud, which gives the conditions for stopping and cooling a fast molecular beam., Comment: 18 pages 11 figures

Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several observables. We propose an implementation of ideas that go back to John von Neumann's writing about the macroscopic measurement. We apply our scheme to the relation between macroscopic autonomy and an H-theorem, and to the problem of equivalence of ensembles. In particular, we show how the latter is related to the asymptotic equipartition theorem. The main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate, as the size of the system gets larger, on the macroscopic values for the different macroscopic observables. Deviations from that law are governed by the entropy., Comment: 16 pages; v1 -> v2: Sec. 3 slightly rewritten, 2 references added

Non-Fellerian processes show phenomena that are unseen in standard interacting particle systems. We consider freezing transitions in one-dimensional non-Fellerian processes which are built from the abelian sandpile additions to which in one case, spin flips are added, and in another case, the so called anti-sandpile subtractions. In the first case and as a function of the sandpile addition rate, there is a sharp transition from a non-trivial invariant measure to the invariant measure of the sandpile process. For the combination sandpile plus anti-sandpile, there is a sharp transition from one frozen state to the other anti-state

The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy. If for a Hamiltonian dynamics for many particles, at all times the present macrostate determines the future macrostate, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autonomous macroscopic evolution (sharp only in the limit of infinite scale separation); and to evaluate the presumed necessity of a Markov property for the macroscopic evolution., Comment: 13 pages; v1 -> v2: Sec. 1-2 considerably rewritten, minor corrections in Sec. 3-4

We consider the q=4 Potts model on the square lattice with an additional hard-core nonlocal interaction. That interaction arises from the choice of the reference measure taken to be the uniform measure on the recurrent configurations for the abelian sandpile model. In that reference measure some correlation functions have a power-law decay. We investigate the low-temperature phase diagram and we prove the existence of a single stable phase with exponential decay of correlations. For all boundary conditions the density of 4 in the infinite volume limit goes to one as the temperature tends to zero.

We introduce a unitary dynamics for quantum spins which is an extension of a model introduced by Mark Kac to clarify the phenomenon of relaxation to equilibrium. When the number of spins gets very large, the magnetization satisfies an autonomous equation as function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proven as a law of large numbers with respect to a class of initial data. The corresponding Gibbs-von Neumann entropy is also computed and its monotonicity in time discussed., Comment: 15 pages, v2 -> v3: minor typographic correction

We consider conservative quantum evolutions possibly interrupted by macroscopic measurements. When started in a nonequilibrium state, the resulting path-space measure is not time-reversal invariant and the weight of time-reversal breaking equals the exponential of the entropy production. The mean entropy production can then be expressed via a relative entropy on the level of histories. This gives a partial extension of the result for classical systems, that the entropy production is given by the source term of time-reversal breaking in the path-space measure., Comment: 11 pages

There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phase-space contraction and time-reversal starting from a deterministic dynamics. Both closed and open systems, in the transient and in the steady regime, are considered. The main result identifies under general conditions the statistical mechanical entropy production as the source term of time-reversal breaking in the path space measure for the evolution of reduced variables. This provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful (in)equalities. We also discuss the Markov approximation. Important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior., Comment: 39 pages, no figures

We show for a large class of interacting particle systems that whenever the stationary measure is not reversible for the dynamics, then the mean entropy production in the steady state is strictly positive. This extends to the thermodynamic limit the equivalence between microscopic reversibility and zero mean entropy production: time-reversal invariance cannot be spontaneously broken., Comment: To appear in the Journal of Statistical Physics (2002)

It is argued that a Gibbsian formula for the space-time distribution of microscopic trajectories of a nonequilibrium system provides a unifying framework for recent results on the fluctuations of the entropy production. The variable entropy production is naturally expressed as the time-reversal symmetry breaking part of the space-time action functional. Its mean is always positive. This is both supported by a Boltzmann type analysis by counting the change in phase space extension corresponding to the macrostate as by various examples of nonequilibrium models. As the Gibbsian set-up allows for non-Markovian dynamics, we also get a local fluctuation theorem for the entropy production in globally Markovian models. In order to study the response of the system to perturbations, we can apply the standard Gibbs formalism., Comment: Corrected typos and some minor additional comments

We point out that the "disorder potential" employed in the grand ensemble approach is ill-defined in considerable generality., Comment: to appear in Phys. Rev. Lett

This is a (long) survey about applications of percolation theory in equilibrium statistical mechanics. The chapters are as follows: 1. Introduction 2. Equilibrium phases 3. Some models 4. Coupling and stochastic domination 5. Percolation 6. Random-cluster representations 7. Uniqueness and exponential mixing from non-percolation 8. Phase transition and percolation 9. Random interactions 10. Continuum models, Comment: 118 pages. Addresses: georgii@rz.mathematik.uni-muenchen.de http://www.mathematik.uni-muenchen.de/~georgii.html olleh@math.chalmers.se http://www.math.chalmers.se/~olleh Christian.Maes@fys.kuleuven.ac.be

Considering the standard abelian sandpile model in one dimension, we construct an infinite volume Markov process corresponding to its thermodynamic (infinite volume) limit. The main difficulty we overcome is the strong non-locality of the dynamics. However, using similar ideas as in recent extensions of the standard Gibbs formalism for lattice spin systems, we can identify a set of `good' configurations on which the dynamics is effectively local. We prove that every configuration converges in a finite time to the unique invariant measure.

We discuss the status of recent Gibbsian descriptions of the restriction (projection) of the Ising phases to a layer. We concentrate on the projection of the two-dimensional low temperature Ising phases for which we prove a variational principle., Comment: 38 pages