exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

lattice gas models in contact with stochastic reservoirs local equilibrium and relaxation to the steady state extending the results of a previous work we consider a class of discrete lattice gas models in a finite interval whose bulk dynamics consists of stochastic exchanges which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials we establish here the local equilibrium structure of the stationary measures for these models further we prove as a law of large numbers that the time dependent empirical density field converges to a deterministic limit process which is the solution of the initial boundary value problem for a nonlinear diffusion equation

direct evaluation of large deviation functions we introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities such as current or density that are local in time the large deviation functions are given in terms of the typical properties of a modified dynamics and since they no longer involve rare events can be evaluated efficiently and over a wider ranges of values we illustrate the method with the current fluctuations of the totally asymmetric exclusion process and with the work distribution of a driven lorentz gas

orthogonal laurent polynomials and strong moment theory a survey these topics are found in many parts of 20th century mathematics and its applications in mathematical physics chemistry statistics and engineering historically the analytic theory of continued fractions has played a central role in both the origin and the development of the other topics continued fractions are intimately related to pad e approximants and special functions emphasis is given to the development of strong moment theory and orthogonal laurent polynomials and to the related continued fractions quadrature formulas integral transforms and linear functionals by a strong moment problem we mean the following for a given bisequence n n of real numbers does there exist a distribution function such that

hydrodynamics of stationary non equilibrium states for some stochastic lattice gas models we consider discrete lattice gas models in a finite interval with stochastic jump dynamics in the interior which conserve the particle number and with stochastic dynamics at the boundaries chosen to model infinite particle reservoirs at fixed chemical potentials the unique stationary measures of these processes support a steady particle current from the reservoir of higher chemical potential into the lower and are non reversible we study the structure of the stationary measure in the hydrodynamic limit as the microscopic lattice size goes to infinity in particular we prove as a law of large numbers that the empirical density field converges to a deterministic limit which is the solution of the stationary transport equation and the empirical current converges to the deterministic limit given by fick s law

entropy of open lattice systems we investigate the behavior of the gibbs shannon entropy of the stationary nonequilibrium measure describing a one dimensional lattice gas of l sites with symmetric exclusion dynamics and in contact with particle reservoirs at different densities in the hydrodynamic scaling limit l the leading order o l behavior of this entropy has been shown by bahadoran to be that of a product measure corresponding to strict local equilibrium we compute the first correction which is o 1 the computation uses a formal expansion of the entropy in terms of truncated correlation functions for this system the k th such correlation is shown to be o l k 1 this entropy correction depends only on the scaled truncated pair correlation which describes the covariance of the density field it coincides in the large l limit with the corresponding correction obtained from a gaussian measure with the same covariance

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

exact large deviation functional of a stationary open driven diffusive system the asymmetric exclusion process we consider the asymmetric exclusion process asep in one dimension on sites i 1 n in contact at sites i 1 and i n with infinite particle reservoirs at densities a and b as a and b are varied the typical macroscopic steady state density profile x x a b obtained in the limit n l b a exhibits shocks and phase transitions here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile rho x text p n rho x sim exp l mathcal f a b rho x rho a rho b so that mathcal f is the large deviation functional a quantity similar to the free energy of equilibrium systems we find as in the symmetric purely diffusive case q 1 treated in an earlier work that mathcal f is in general a non local functional of x unlike the symmetric case however the asymmetric case exhibits ranges of the parameters for which mathcal f rho x is not convex and others for which mathcal f rho x has discontinuities in its second derivatives at x x in the latter ranges the fluctuations of order 1 sqrt n in the density profile near x are then non gaussian and cannot be calculated from the large deviation function

finite size corrections to the large deviation function of the density in the one dimensional symmetric simple exclusion process the symmetric simple exclusion process is one of the simplest out of equilibrium systems for which the steady state is known its large deviation functional of the density has been computed in the past both by microscopic and macroscopic approaches here we obtain the leading finite size correction to this large deviation functional the result is compared to the similar corrections for equilibrium systems

large deviations for a stochastic model of heat flow we investigate a one dimensional chain of 2n harmonic oscillators in which neighboring sites have their energies redistributed randomly the sites n and n are in contact with thermal reservoirs at different temperature and kipnis et al j statist phys 27 65 74 1982 proved that this model satisfies fourier s law and that in the hydrodynamical scaling limit when n the stationary state has a linear energy density profile bar theta u u 1 1 we derive the large deviation function s u for the probability of finding in the stationary state a profile u different from bar theta u the function s has striking similarities to but also large differences from the corresponding one of the symmetric exclusion process like the latter it is nonlocal and satisfies a variational equation unlike the latter it is not convex and the gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state we also briefly discuss more general models and find the features common in these two and other models whose s is known

universal cumulants of the current in diffusive systems on a ring we calculate exactly the first cumulants of the integrated current and of the activity which is the total number of changes of configurations of the symmetric simple exclusion process on a ring with periodic boundary conditions our results indicate that for large system sizes the large deviation functions of the current and of the activity take a universal scaling form with the same scaling function for both quantities this scaling function can be understood either by an analysis of bethe ansatz equations or in terms of a theory based on fluctuating hydrodynamics or on the macroscopic fluctuation theory of bertini de sole gabrielli jona lasinio and landim

thermodynamic transformations of nonequilibrium states we consider a macroscopic system in contact with boundary reservoirs and or under the action of an external field we discuss the case in which the external forcing depends explicitly on time and drives the system from a nonequilibrium state to another one in this case the amount of energy dissipated along the transformation becomes infinite when an unbounded time window is considered 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 we then discuss its thermodynamic relevance by showing that it satisfies a clausius inequality and that quasi static transformations minimize the renormalized work in addition we connect the renormalized work to the quasi potential describing the fluctuations in the stationary nonequilibrium ensemble the latter result provides a characterization of the quasi potential that does not involve rare fluctuations

shape classification using invariant features and contextual information in the bag of words model in this paper we describe a classification framework for binary shapes that have scale rotation and strong viewpoint variations to this end we develop several novel techniques first we employ the spectral magnitude of log polar transform as a local feature in the bag of words model second we incorporate contextual information in the bag of words model using a novel method to extract bi grams from the spatial co occurrence matrix third a novel metric termed weighted gain ratio is proposed to select a suitable codebook size in the bag of words model the proposed metric is generic and hence it can be used for any clustering quality evaluation task fourth a joint learning framework is proposed to learn features in a data driven manner and thus avoid manual fine tuning of the model parameters we test our shape classification system on the animal shapes dataset and significantly outperform state of the art methods in the literature highlightsa shape classifier tolerant to scale rotation and viewpoint changes is proposed the inclusion of the histogram of bi grams improves the bag of words model codebook selection and feature learning improve the classification accuracy we report best results on the animal shapes dataset using the proposed method

solutions of the strong hamburger moment problem abstract the strong hamburger moment problem for a bi infinite sequence c n n 0 1 2 can be described as follows 1 find conditions for the existence of a positive measure on such that c n t n d t for all n 2 when there is a solution find conditions for uniqueness of the solution 3 when there is more than one solution describe the family of all solutions in this paper a theory concerning question 3 is developed in particular an analog to the nevanlinna parametrization describing the solutions of the classical hamburger moment problem is given

large deviation functional of the weakly asymmetric exclusion process we obtain the large deviation functional of a density profile for the asymmetric exclusion process of l sites with open boundary conditions when the asymmetry scales like l 1 we recover as limiting cases the expressions derived recently for the symmetric ssep and the asymmetric asep cases in the asep limit the nonlinear differential equation one needs to solve can be analysed by a method which resembles the wkb method

large deviations in weakly interacting boundary driven lattice gases one dimensional boundary driven lattice gases with local interactions are studied in the weakly interacting limit the density profiles and the correlation functions are calculated to first order in the interaction strength for zero range and short range processes differing only in the specifics of the detailed balance dynamics furthermore the effective free energy large deviation function and the integrated current distribution are also found to this order from the former we find that the boundary drive generates long range correlations only for the short range dynamics while the latter provides support to an additivity principle recently proposed by bodineau and derrida

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

nevanlinna matrices for the strong stieltjes moment problem abstract let c n n be a doubly infinite sequence of real numbers a solution of the strong hamburger moment problem is a positive measure on such that c n u n d u for n 0 1 2 a solution of the strong stieltjes moment problem is a positive measure on 0 such that c n 0 u n d u for n 0 1 2 a moment problem is indeterminate if there exists more than one solution with an indeterminate strong hamburger moment problem there is associated a nevanlinna matrix of functions holomorphic in ofc 0 these functions have growth properties partly similar to properties of analogous entire functions associated with an indeterminate classical hamburger moment problem in this paper we obtain a stronger growth result in the case where the strong stieltjes moment problem is solvable

minimum dissipation principle in stationary non equilibrium states we generalize to non equilibrium states onsager s minimum dissipation principle we also interpret this principle and some previous results in terms of optimal control theory entropy production plays the role of the cost necessary to drive the system to a prescribed macroscopic configuration

large deviation of the density profile in the steady state of the open symmetric simple exclusion process we consider an open one dimensional lattice gas on sites i 1 n with particles jumping independently with rate 1 to neighboring interior empty sites the simple symmetric exclusion process the particle fluxes at the left and right boundaries corresponding to exchanges with reservoirs at different chemical potentials create a stationary nonequilibrium state sns with a steady flux of particles through the system the mean density profile in this state which is linear describes the typical behavior of a macroscopic system i e this profile occurs with probability 1 when n the probability of microscopic configurations corresponding to some other profile x x i n has the asymptotic form exp n f f is the large deviation functional in contrast to equilibrium systems for which f eq is just the integral of the appropriately normalized local free energy density the f we find here for the nonequilibrium system is a nonlocal function of this gives rise to the long range correlations in the sns predicted by fluctuating hydrodynamics and suggests similar non local behavior of f in general sns where the long range correlations have been observed experimentally