Clausius inequality and optimality of quasi static transformations for nonequilibrium stationary states

Nonequilibrium stationary states of thermodynamic systems dissipate a positive amount of energy per unit of time. If we consider transformations of such states that are realized by letting the driving depend on time, the amount of energy dissipated in an unbounded time window becomes then infinite. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work performed along any given transformation. We then show that the renormalized work satisfies a Clausius inequality and prove that equality is achieved for very slow transformations, that is in the quasi static limit. We finally connect the renormalized work to the quasi potential of the macroscopic fluctuation theory, that gives the probability of fluctuations in the stationary nonequilibrium ensemble

Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Percolation in real Wildfires

This paper focuses on the statistical properties of wild-land fires and, in particular, investigates if spread dynamics relates to simple invasion model. The fractal dimension and lacunarity of three fire scars classified from satellite imagery are analysed. Results indicate that the burned clusters behave similarly to percolation clusters on boundaries and look more dense in their core. We show that Dynamical Percolation reproduces this behaviour and can help to describe the fire evolution. By mapping fire dynamics onto the percolation models the strategies for fire control might be improved.Comment: 8 pages, 3 figures, epl sytle (epl.cls included

The Strong-Coupling Expansion in Simplicial Quantum Gravity

We construct the strong-coupling series in 4d simplicial quantum gravity up to volume 38. It is used to calculate estimates for the string susceptibility exponent gamma for various modifications of the theory. It provides a very efficient way to get a first view of the phase structure of the models.Comment: LATTICE98(surfaces), 3 pages, 4 eps figure

Diffusion, super-diffusion and coalescence from single step

From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field \bu(\bx), we derive different dynamical regimes when \bu(\bx) is iterated to build a velocity field. First we show that spatially uncorrelated fields \bu(\bx) lead to both standard and anomalous diffusion equation. When the field \bu(\bx) is spatially correlated each particle performs a simple free Brownian motion, but the trajectories of different particles result to be mutually correlated. The two-point statistical properties of the field \bu(\bx) induce two-point spatial correlations in the particle distribution satisfying a simple but non-trivial diffusion-like equation. These displacement-displacement correlations lead the system to three possible regimes: coalescence, simple clustering and a combination of the two. The existence of these different regimes, in the one-dimensional system, is shown through computer simulations and a simple theoretical argument.Comment: RevTeX (iopstyle) 19 pages, 5 eps-figure

Initial conditions, Discreteness and non-linear structure formation in cosmology

In this lecture we address three different but related aspects of the initial continuous fluctuation field in standard cosmological models. Firstly we discuss the properties of the so-called Harrison-Zeldovich like spectra. This power spectrum is a fundamental feature of all current standard cosmological models. In a simple classification of all stationary stochastic processes into three categories, we highlight with the name ``super-homogeneous'' the properties of the class to which models like this, with $P(0)=0$, belong. In statistical physics language they are well described as glass-like. Secondly, the initial continuous density field with such small amplitude correlated Gaussian fluctuations must be discretised in order to set up the initial particle distribution used in gravitational N-body simulations. We discuss the main issues related to the effects of discretisation, particularly concerning the effect of particle induced fluctuations on the statistical properties of the initial conditions and on the dynamical evolution of gravitational clustering.Comment: 28 pages, 1 figure, to appear in Proceedings of 9th Course on Astrofundamental Physics, International School D. Chalonge, Kluwer, eds N.G. Sanchez and Y.M. Pariiski, uses crckapb.st pages, 3 figure, ro appear in Proceedings of 9th Course on Astrofundamental Physics, International School D. Chalonge, Kluwer, Eds. N.G. Sanchez and Y.M. Pariiski, uses crckapb.st

Gravitational Dynamics of an Infinite Shuffled Lattice: Particle Coarse-grainings, Non-linear Clustering and the Continuum Limit

We study the evolution under their self-gravity of infinite ``shuffled lattice'' particle distributions, focussing specifically on the comparison of this evolution with that of ``daughter'' particle distributions, defined by a simple coarse-graining procedure. We consider both the case that such coarse-grainings are performed (i) on the initial conditions, and (ii) at a finite time with a specific additional prescription. In numerical simulations we observe that, to a first approximation, these coarse-grainings represent well the evolution of the two-point correlation properties over a significant range of scales. We note, in particular, that the form of the two-point correlation function in the original system, when it is evolving in the asymptotic ``self-similar'' regime, may be reproduced well in a daughter coarse-grained system in which the dynamics are still dominated by two-body (nearest neighbor) interactions. Using analytical results on the early time evolution of these systems, however, we show that small observed differences between the evolved system and its coarse-grainings at the initial time will in fact diverge as the ratio of the coarse-graining scale to the original inter-particle distance increases. The second coarse-graining studied, performed at a finite time in a specified manner, circumvents this problem. It also makes more physically transparent why gravitational dynamics from these initial conditions tends toward a ``self-similar'' evolution. We finally discuss the precise definition of a limit in which a continuum (specifically Vlasov-like) description of the observed linear and non-linear evolution should be applicable.Comment: 21 pages, 8 eps figures, 2 jpeg figures (available in high resolution at http://pil.phys.uniroma1.it/~sylos/PRD_dec_2006/

Lagrangian phase transitions in nonequilibrium thermodynamic systems

In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in nonequilibrium this is not necessarily the case. We show that in nonequilibrium a new type of singularities can appear that are interpreted as phase transitions. In particular, this phenomenon occurs for the one-dimensional boundary driven weakly asymmetric exclusion process when the drift due to the external field is opposite to the one due to the external reservoirs, and strong enough.Comment: 10 pages, 2 figure

Effective Yukawa couplings and flavor-changing Higgs boson decays at linear colliders

We analyze the advantages of a linear-collider program for testing a recent theoretical proposal where the Higgs-boson Yukawa couplings are radiatively generated, keeping unchanged the standard-model mechanism for electroweak-gauge-symmetry breaking. Fermion masses arise at a large energy scale through an unknown mechanism, and the standard model at the electroweak scale is regarded as an effective field theory. In this scenario, Higgs boson decays into photons and electroweak gauge-boson pairs are considerably enhanced for a light Higgs boson, which makes a signal observation at the LHC straightforward. On the other hand, the clean environment of a linear collider is required to directly probe the radiative fermionic sector of the Higgs boson couplings. Also, we show that the flavor-changing Higgs-boson decays are dramatically enhanced with respect to the standard model. In particular, we find a measurable branching ratio in the range (10^{-4}-10^{-3}) for the decay H\to bs for a Higgs boson lighter than 140 GeV, depending on the high-energy scale where Yukawa couplings vanish. We present a detailed analysis of the Higgs boson production cross sections at linear colliders for interesting decay signatures, as well as branching-ratio correlations for different flavor-conserving/nonconserving fermionic decays.Comment: 23 pages, 7 figures, 5 table

Growing Cayley trees described by Fermi distribution

We introduce a model for growing Cayley trees with thermal noise. The evolution of these hierarchical networks reduces to the Eden model and the Invasion Percolation model in the limit $T\to 0$, $T\to \infty$ respectively. We show that the distribution of the bond strengths (energies) is described by the Fermi statistics. We discuss the relation of the present results with the scale-free networks described by Bose statistics