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

Symmetries in Fluctuations Far from Equilibrium

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.Comment: 8 pages, 4 figure

Anthropometric features and body composition of young athletes practicing karate at a high and medium competitive level

The aim of the study was to examine the anthropometric features and body composition of athletes practising karate at a high and medium competitive level. Our study was carried out on a sample of 35 subjects practising karate and aged from 16.0 to 32.5 years. This sample was divided into two groups: group 1 (n=14 elite athletes) and group 2 (n=21 amateur athletes). Various anthropometric measurements were taken (weight, height both standing and sitting, diameters, circumferences and skinfold thickness) from which different anthropometric indices were calculated (body mass index, Scelic and Grant indices, arm muscle circumference and area), and the somatotype was then determined. The body composition of each subject was assessed using the skinfold technique and the Jackson-Pollock (J-P) and Sloan-Weir (S-W) equations. The two groups of athletes showed very similar measurements regarding anthropometric characteristics. Only the Scelix index presented a significantly different value in the two groups (49.6±1.3 for group 1 vs. 51.1±1.3 for group 2; p<0.01). Group 1 showed a mesomorphic-ectomorphic somatotype, while the amateur athletes presented a balanced mesomorphic type. Moreover, a lower percentage of fat mass was more frequent in the first group (J-P=8.1±2.4%; S-W=8.9±3.3%) than in the second one (J-P=9.8±1.6%; S-W=11.2±3.7%), although the differences between the two groups were not significant. We conclude that group 1 is characterized by a slightly prominent vertical development of the skeletal frame. This could be an anthropometric characteristic that is best suited to meet the specific functional requirements of this sport. Moreover, both groups of athletes are characterized by a low percentage of fat mass, particularly the elite group

Dynamics and Lax-Phillips scattering for generalized Lamb models

This paper treats the dynamics and scattering of a model of coupled oscillating systems, a finite dimensional one and a wave field on the half line. The coupling is realized producing the family of selfadjoint extensions of the suitably restricted self-adjoint operator describing the uncoupled dynamics. The spectral theory of the family is studied and the associated quadratic forms constructed. The dynamics turns out to be Hamiltonian and the Hamiltonian is described, including the case in which the finite dimensional systems comprises nonlinear oscillators; in this case the dynamics is shown to exist as well. In the linear case the system is equivalent, on a dense subspace, to a wave equation on the half line with higher order boundary conditions, described by a differential polynomial $p(\partial_x)$ explicitely related to the model parameters. In terms of such structure the Lax-Phillips scattering of the system is studied. In particular we determine the incoming and outgoing translation representations, the scattering operator, which turns out to be unitarily equivalent to the multiplication operator given by the rational function $-p(i\kappa)^*/p(i\kappa)$, and the Lax-Phillips semigroup, which describes the evolution of the states which are neither incoming in the past nor outgoing in the future

Soft and hard wall in a stochastic reaction diffusion equation

We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two stable phases, as the intensity of the noise vanishes and the size of the interval diverges. In particular, we prove that, in a suitable scaling limit, the front evolves according to a one-dimensional diffusion process with a non-linear drift accounting for a "soft" repulsion from the boundary. We finally show how a "hard" repulsion can be obtained by an extra diffusive scaling.Comment: 33 page

SOFTWARE FOR WEATHER DATABASES MANAGEMENT AND CONSTRUCTION OF REFERENCE YEARS

The purpose of this paper is to illustrate a procedure that permits, starting from a sufficiently long database of time series, the construction of a Reference Year (RY) of hourly weather data according to the rules of ISO 15927-4 standard. In order to facilitate the management of the weather database and to allow the users to easily generate the file, an algorithm has been implemented in Microsoft Visual Basic for Application (VBA). By this way, the application of the ISO 15927-4 is possible even using a popular software tool such as Microsoft Excel or Access without any other expensive specialized software. Such tool allows to fulfil all the procedures mentioned in ISO 15927- 4 giving as result a time series of 8760 values of several weather variables, ready to be used in any software for energy simulation of buildings

Rigorous Dynamics and Radiation Theory for a Pauli-Fierz Model in the Ultraviolet Limit

The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behaviour of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behaviour is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibites in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator.Comment: Shortened version. To appear in J. Math. Phy

Macroscopic fluctuation theory

Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics approach, these states have been the subject of several theoretical investigations, both analytic and numerical. The macroscopic fluctuation theory, based on a formula for the probability of joint space-time fluctuations of thermodynamic variables and currents, provides a unified macroscopic treatment of such states for driven diffusive systems. We give a detailed review of this theory including its main predictions and most relevant applications.Comment: Review article. Revised extended versio

Stochastic interacting particle systems out of equilibrium

This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a unified picture is emerging at the macroscopic level, applicable, in our view, to real phenomena where diffusion is the dominating physical mechanism. We rely mainly on an approach developed by the authors based on the study of dynamical large fluctuations in stationary states of open systems. The outcome of this approach is a theory connecting the non equilibrium thermodynamics to the transport coefficients via a variational principle. This leads ultimately to a functional derivative equation of Hamilton-Jacobi type for the non equilibrium free energy in which local thermodynamic variables are the independent arguments. In the first part of the paper we give a detailed introduction to the microscopic dynamics considered, while the second part, devoted to the macroscopic properties, illustrates many consequences of the Hamilton-Jacobi equation. In both parts several novelties are included.Comment: 36 page

The Pomeron and Odderon in elastic, inelastic and total cross sections at the LHC

A simple model for elastic diffractive hadron scattering, reproducing the dip-bump structure is used to analyze PP and $\bar PP$ scattering. The main emphasis is on the delicate and non-trivial dynamics in the dip-bump region, near t=-1 GeV$^2$. The simplicity of the model and the expected smallness of the absorption corrections enables one the control of various contributions to the scattering amplitude, in particular the interplay between the C-even and C-odd components of the amplitude, as well as their relative contribution, changing with s and t. The role of the non-linearity of the Regge trajectories is scrutinized. The ratio of the real to imaginary parts of the forward amplitude, the ratio of elastic to total cross sections and the inelastic cross section are calculated. Predictions for the LHC energy region, where most of the exiting models will be either confirmed or ruled out, are presented.Comment: 16 pages, 13 figures. Small correction. To be published in the International Journal of Modern Physics