metastability and small eigenvalues in markov chains in this letter we announce rigorous results that elucidate the relation between metastable states and low lying eigenvalues in markov chains in a much more general setting and with considerably greater precision than has so far been available this includes a sharp uncertainty principle relating all low lying eigenvalues to mean times of metastable transitions a relation between the support of eigenfunctions and the attractor of a metastable state and sharp estimates of the convergence of the probability distribution of the metastable transition times to the exponential distribution

note on two theorems in nonequilibrium statistical mechanics an attempt is made to clarify the difference between a theorem derived by evans and searles in 1994 on the statistics of trajectories in phase space and a theorem proved by the authors in 1995 on the statistics of fluctuations on phase space trajectory segments in a nonequilibrium stationary state

characterisation of intermittency in chaotic systems the authors discuss the characterisation of intermittency in chaotic dynamical systems by means of the time fluctuations of the response to a slight perturbation on the trajectory a set of exponents is introduced which generalise the maximum lyapunov characteristic exponent the link with the statistical mechanics formalism is emphasised and they show that the exponents are connected to a free energy formally defined for chaotic systems they perform some analytical computations in simple cases and give a few numerical examples

metastable states in glassy systems truly stable metastable states are an artifact of the mean field approximation or the zero temperature limit if such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations one needs to cast them in a form involving states with finite lifetimes starting from elementary examples and using the results of gaveau and schulman we propose a simple expression for the configurational entropy and revisit the question of taking flat averages over metastable states the construction is applicable to finite dimensional systems and we explicitly show that for simple mean field glass models it recovers justifies and generalizes the known results the calculation emphasises the appearance of new dynamical order parameters

large deviations metastability and selection abstract in this note i introduce some techniques to treat systems in contact with stochastic thermal baths the methods and the level of rigour are those of theoretical physics

parametrized singular boundary value problems abstract certain types of singular ordinary differential equations depending on parameters are studied lower bounds of the number of parameters are found for which those equations possess a positive solution for this purpose the nielsen fixed point theory is used

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

nontrivial application of nielsen theory to differential systems in reply to a problem of jean leray concerning application of the nielsen theory to differential systems for obtaining multiplicity results we present a nontrivial example of such an application the emphasis is on the parameter space in order to ensure that no subdomain becomes subinvariant under the related hammerstein solution operator to achieve this goal we develop a general method applicable also for ordinary differential equations with or without uniqueness as well as for upper caratheodory differential inclusions we are not aware that any alternative approach can be employed even in the single valued case

locality and orthomodular structure of compound systems a p lattice is defined as a complete orthomodular atomic lattice l which is formed by the set of propositions of a physical system a composition of physical systems in the framework of p lattices is considered and some notions of locality are given it is shown that the following statements about compound systems are equivalent a all atoms of a compound system are reducible to those of its subsystems b all pure states of a compound system are separable into those of its subsystems c a compound system has statistical property independence d at least one of the subsystems is classical e bell type inequalities hold

equilibrium fluctuations for a system of harmonic oscillators with conservative noise we investigate the harmonic chain forced by a multiplicative noise the evolution is given by an infinite system of stochastic differential equations total energy and deformation are preserved the conservation of momentum is destroyed by the noise gaussian product measures are the extremal stationary states of this model equilibrium fluctuations of the conserved fields at a diffusive scaling are described by a couple of generalized ornstein uhlenbeck processes

hidden variables in quantum logic approach reexamined various impossibility proofs for hidden variables theories produced within the quantum logic approach are analyzed a very general form of n term bell type inequalities is given from these inequalities a new impossibly proof for hidden variables theories able to reproduce all numerical results of quantum mechanics follows

information theoretic bell inequalities we formulate information theoretic bell inequalities which apply to any pair of widely separated physical systems if local realism holds the two systems must carry information consistent with the inequalities two spin s particles in a state of zero total spin violate these information bell inequalities

gallavotti cohen theorem chaotic hypothesis and the zero noise limit the fluctuation relation for a stationary state kept at constant energy by a deterministic thermostat the gallavotti cohen theorem relies on the ergodic properties of the system considered we show that when perturbed by an energy conserving random noise the relation follows trivially for any system at finite noise amplitude the time needed to achieve stationarity may stay finite as the noise tends to zero or it may diverge in the former case the gallavotti cohen result is recovered while in the latter case the crossover time may be computed from the action of instanton orbits that bridge attractors and repellors we suggest that the chaotic hypothesis of gallavotti cohen and ruelle can thus be reformulated as a matter of stochastic stability of the measure in trajectory space in this form this hypothesis may be directly tested

tunnelling in near integrable systems tunnelling rates are qualitatively different for integrable and near integrable systems here a uniform result is derived which interpolates between the two regimes and is applied successfully to two dimensional double well and pendulum potentials when the underlying symmetry is reflection in a single coordinate the splitting remains positive after perturbation but for potentials whose underlying symmetry is reflection through the origin the splitting is predicted to oscillate as a function of a perturbation parameter with regularly spaced zeros where tunnelling switches off

reversibility coarse graining and the chaoticity principle we describe a way of interpreting the chaotic principle of gc1 more extensively than it was meant in the original works mathematically the analysis is based on the dynamical notions of axiom a and axiom b and on the notion of axiom c that we introduce arguing that it is suggested by the results of an experiment bgg on chaotic motions physically we interpret a breakdown of the anosov property of a time reversible attractor replaced as a control parameter changes by an axiom a property as a spontaneous breakdown of the time reversal symmetry the relation between time reversal and the symmetry that remains after the breakdown is analogous to the breakdown of t invariance while tcp still holds

bell inequalities on quantum logics three types of bell inequalities expressed in terms of quantum logics orthomodular lattices and states on them are studied it is shown that the two first types are equivalent to the subadditivity of the corresponding state the third type is equivalent to the existence of a boolean quotient b of the orthomodular lattice l and a state s on b such that s s where s is the state on l and l b is the quotient mapping

monotone iterative techniques for parameterized bvps of abstract semilinear evolution equations abstract this paper is concerned with parameterized boundary value problems bvps for semilinear evolution equations in a general banach space the abstract monotone iterative schemes are constructed by combining the theory of semigroups of operators and the method of upper and lower solutions some existence results are established under the suitable conditions applications to periodic bvps with a parameter and parabolic partial differential equations are also given to illustrate the main results

boundary value problems for first order impulsive delay differential equations with a parameter in this paper by means of the method of upper and lower solutions and monotone iterative technique the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established