Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an underlying microscopic dynamics: the only input required are transport coefficients as functions of thermodynamic variables, which are experimentally accessible. The basic postulates are local equilibrium which allows a hydrodynamic description of the evolution, the Einstein relation among the transport coefficients, and a variational principle defining the out of equilibrium free energy. Associated to the variational principle there is a Hamilton-Jacobi equation satisfied by the free energy, very useful for concrete calculations. Correlations over a macroscopic scale are, in our scheme, a generic property of nonequilibrium states. Correlation functions of any order can be calculated from the free energy functional which is generically a non local functional of thermodynamic variables. Special attention is given to the notion of equilibrium state from the standpoint of nonequilibrium.Comment: 21 page

Attracting and Retaining Women in the Transportation Industry

This study synthesized previously conducted research and identified additional research needed to attract, promote, and retain women in the transportation industry. This study will detail major findings and subsequent recommendations, based on the annotated bibliography, of the current atmosphere and the most successful ways to attract and retain young women in the transportation industry in the future. Oftentimes, it is perception that drives women away from the transportation industry, as communal goals are not emphasized in transportation. Men are attracted to agentic goals, whereas women tend to be more attracted to communal goals (Diekman et al., 2011). While this misalignment of goals has been found to be one reason that women tend to avoid the transportation industry, there are ways to highlight the goal congruity processes that contribute to transportation engineering, planning, operations, maintenance, and decisions—thus attracting the most talented individuals, regardless of gender. Other literature has pointed to the lack of female role models and mentors as one reason that it is difficult to attract women to transportation (Dennehy & Dasgupta, 2017). It is encouraging to know that attention is being placed on the attraction and retention of women in all fields, as it will increase the probability that the best individual is attracted to the career that best fits their abilities, regardless of gender

On the Euler angles for SU(N)

In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU(N) and then we determine the full range of the parameters, using both topological and geometrical methods. In particular, we show that the given parametrization realizes the group $SU(N+1)$ as a fibration of U(N) over the complex projective space $\mathbb{CP}^n$. This justifies the interpretation of the parameters as generalized Euler angles.Comment: 16 pages, references adde

Non equilibrium current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation $j$ of the empirical current with a rate functional \mc I (j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional \mc I . We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of \mc I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.Comment: 36 Pages, No figur

Level 2.5 large deviations for continuous time Markov chains with time periodic rates

We consider an irreducible continuous time Markov chain on a finite state space and with time periodic jump rates and prove the joint large deviation principle for the empirical measure and flow and the joint large deviation principle for the empirical measure and current. By contraction we get the large deviation principle of three types of entropy production flow. We derive some Gallavotti-Cohen duality relations and discuss some applications.Comment: 37 pages. corrected versio

Renormalization Group in the uniqueness region: weak Gibbsianity and convergence

We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. We prove weak Gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense. Since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system: the correlation length or the critical length for metastability, or both. Thus, to perturbatively treat the problem we have to use a scale-adapted expansion. Moreover, such a model below the critical temperature resembles a disordered system in presence of Griffiths' singularity. Then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached

Perturbative analysis of disordered Ising models close to criticality

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion implies the infinite differentiability of the free energy but not its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder