Nonequilibrium Statistical Mechanics and Entropy Production in a Classical Infinite System of Rotators

We analyze the dynamics of a simple but nontrivial classical Hamiltonian system of infinitely many coupled rotators. We assume that this infinite system is driven out of thermal equilibrium either because energy is injected by an external force (Case I), or because heat flows between two thermostats at different temperatures (Case II). We discuss several possible definitions of the entropy production associated with a finite or infinite region, or with a partition of the system into a finite number of pieces. We show that these definitions satisfy the expected bounds in terms of thermostat temperatures and energy flow.     

SRB States and Nonequilibrium Statistical Mechanics Close to Equilibrium

Nonequilibrium statistical mechanics close to equilibrium is studied using SRB states and a formula [10] for their derivatives with respect to parameters. We write general expressions for the thermodynamic fluxes (or currents) and the transport coefficients, generalizing the results of [4, 5]. In this framework we give a general proof of the Onsager reciprocity relations. Received: 2 December 1996 / Accepted: 13 March 1997     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

Sharp determinants

We introduce a sharp trace Tr^# and a sharp determinant Det^#(1-z) for an algebra of operators acting on functions of bounded variation on the real line. We show that the zeroes of the sharp determinant describe the discrete spectrum of . The relationship with weighted zeta functions of interval maps and Milnor-Thurston kneading determinants is explained. This yields a result on convergence of the discrete spectrum of approximated operators.Oblatum 8-V-1995 & IX-1995On leave from CNRS, UMR 128, ENS Lyon, France     

Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water

Summary The thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability bility constant K_o which can be derived from solubility data. At 25°C, this constant amounts to 80 cm³/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.     

Must thermodynamic functions be piecewise analytic?

There seems to be no general theoretical argument to support the idea that thermodynamic functions are piecewise analytic. We suggest that nonanalyticity may be associated with Gibbs states which are quasiperiodic under space translations, or have a more general nonperiodic (turbulent) behavior.     

Ergodic theory of differentiable dynamical systems

Iff is a C^{1 + ɛ} diffeomorphism of a compact manifold M, we prove the existence of stable manifolds, almost everywhere with respect to everyf-invariant probability measure on M. These stable manifolds are smooth but do not in general constitute a continuous family. The proof of this stable manifold theorem (and similar results) is through the study of random matrix products (multiplicative ergodic theorem) and perturbation of such products. Dedicated to the memory of Rufus Bowen     

Logarithmic conformal field theory and boundary effects in the dimer model

We study the finite-size corrections of the dimer model on a square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of ; we also show that such unusual finite-size behavior can be fully explained in the framework of the logarithmic conformal field theory.     

Rapid identification of environmental bacterial strains by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

In recent years, various mass spectrometry procedures have been developed for bacterial identification. The accuracy and speed with which data can be obtained by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) could make this a powerful tool for environmental monitoring. However, minor variations in the sample preparation can influence the mass spectra significantly. Therefore, the first objectives of this study were the adjustment and the optimization of experimental parameters allowing a rapid identification of whole bacterial cells without laborious sample preparation. The tested experimental parameters were matrix, extraction solvent, salt content, deposition method, culture medium and incubation time. This standardized protocol was applied to identify reference and environmental bacterial strains of Escherichia coli, Salmonella and Acinetobacter. The environmental bacterial strains were isolated from sewage sludge using an original microextraction procedure based on repeated sonications and enzymatic treatments. The bacterial identification was realized by the observation of the respective genus-, species- and strain-specific biomarkers. This bacterial taxonomy could be completed within one hour, with minimal sample preparation, provided that sufficient bacteria had been collected prior to MALDI-TOF analysis.     

Entropy Production in Nonequilibrium Statistical Mechanics

We consider systems of nonequilibrium statistical mechanics, driven by nonconservative forces and in contact with an ideal thermostat. These are smooth dynamical systems for which one can define natural stationary states μ (SRB in the simplest case) and entropy production e(μ) (minus the sum of the Lyapunov exponents in the simplest case). We give exact and explicit definitions of the entropy production e(μ) for the various situations of physical interest. We prove that e(μ)≥0 and indicate cases where e(μ)>0. The novelty of the approach is that we do not try to compute entropy production directly, but make it depend on the identification of a natural stationary state for the system. Received: 15 July 1996 / Accepted: 30 October 1996