dynamic localization of lyapunov vectors in hamiltonian lattices the convergence of the lyapunov vector toward its asymptotic shape is investigated in two different one dimensional hamiltonian lattices the so called fermi pasta ulam and phi 4 chains in both cases we find an anomalous behavior i e a clear difference from the previously conjectured analogy with the kardar parisi zhang equation the origin of the discrepancy is eventually traced back to the existence of nontrivial long range correlations both in space and time as a consequence of this anomaly we find that in a hamiltonian lattice the largest lyapunov exponent is affected by stronger finite size corrections than standard space time chaos

a family of symplectic integrators stability accuracy and molecular dynamics applications the following integration methods for special second order ordinary differential equations are studied leapfrog implicit midpoint trapezoid stormer verlet and cowell numerov we show that all are members or equivalent to members of a one parameter family of schemes some methods have more than one common form and we discuss a systematic enumeration of these forms we also present a stability and accuracy analysis based on the idea of modified equations and a proof of symplecticness it follows that cowell numerov and lim2 a method proposed by zhang and schlick are symplectic a different interpretation of the values used by these integrators leads to higher accuracy and better energy conservation hence we suggest that the straightforward analysis of energy conservation is misleading

an application of gauge theory to four dimensional topology soit x une u variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee q est definie positive alors cette forme est equivalente sur les entiers a la forme diagonale standard soit dans une base q u 1 u 2 u 2 u 2 1 u 2 2 u 2 2

the gallavotti cohen fluctuation theorem for a non chaotic model we test the applicability of the gallavotti cohen fluctuation formula on a nonequilibrium version of the periodic ehrenfest wind tree model this is an one particle system whose dynamics is rather complex e g it appears to be diffusive at equilibrium but its lyapunov exponents are nonpositive for small applied field the system exhibits a very long transient during which the dynamics is roughly chaotic followed by asymptotic collapse on a periodic orbit during the transient the dynamics is diffusive and the fluctuations of the current are found to be in agreement with the fluctuation formula despite the lack of real hyperbolicity these results also constitute an example which manifests the difference between the fluctuation formula and the evans searles identity

chaotic principle an experimental test abstract the chaotic hypothesis discussed in gallavotti and cohen 1995 is tested experimentally in a simple conduction model besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which as the forcing strength grows the attractor ceases to be an anosov system and becomes an axiom a attractor a first text of new predictions is also attempted

chaotic hypothesis onsager reciprocity and fluctuation dissipation theorem it is shown that the chaoticity hypothesis recently introduced in statistical mechanics which is analogous to ruelle s principle for turbulence implies the onsager reciprocity and the fluctuation dissipation theorem in various reversible models for coexisting transport phenomena

liapunov exponents in high dimensional symplectic dynamics the existence of a thermodynamic limit of the distribution of liapunov exponents is numerically verified in a large class of symplectic models ranging from hamiltonian flows to maps and products of random matrices in the highly chaotic regime this distribution is approximately model independent near an integrable limit only a few exponents give a relevant contribution to the kolmogorov sinai entropy

on the validity of the conjugate pairing rule for lyapunov exponents for hamiltonian systems subject to an external potential which in the presence of a thermostat will reach a nonequilibrium stationary state dettmann and morriss proved a strong conjugate pairing rule scpr for pairs of lyapunov exponents in the case of isokinetic ik stationary states which have a given kinetic energy this scpr holds for all initial phases of the system all times t and all numbers of particles n this proof was generalized by wojtkowski and liverani to include hard interparticle potentials a geometrical reformulation of those results is presented the present paper proves numerically using periodic orbits for the lorentz gas that scpr cannot hold for isoenergetic ie stationary states which have a given total internal energy in that case strong evidence is obtained for cpr to hold for large n and t where it can be conjectured that the larger n the smaller t will be this suffices for statistical mechanics

molecular dynamics smoothed particle applied mechanics and irreversibility abstract we explore the relationship of monaghan s version of smoothed particle hydrodynamics here called smoothed particle applied mechanics to nonequilibrium molecular dynamics we first use smoothed particles to model the simplest possible linear transport problems as well as a liquid drop problem we then consider both gas phase and dense fluid versions of rayleigh benard convection all in two space dimensions we also discuss the possibility of combining the microscopic and macroscopic techniques in a hybrid scheme well suited to the massively parallel modelling of large scale nonequilibrium flows

structure of characteristic lyapunov vectors in anharmonic hamiltonian lattices in this work we perform a detailed study of the scaling properties of lyapunov vectors lvs for two different one dimensional hamiltonian lattices the fermi pasta ulam and 4 models in this case characteristic also called covariant lvs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal in contrast backward lvs obtained via gram schmidt orthonormalizations present approximately the same scaling exponent in all cases suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors we are able to compute characteristic lvs in large systems thanks to a bit reversible algorithm which completely obviates computer memory limitations

on the fluctuation relation for nose hoover boundary thermostated systems we discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures the system is a modified lorentz gas in which the fixed scatterers exchange energy with the gas of particles and the thermostats are modelled by two nose hoover thermostats applied at the boundaries of the system the transient fluctuation relation which holds only for a precise choice of the initial ensemble is verified at all times as expected times longer than the mesoscopic scale needed for local equilibrium to be settled are required if a different initial ensemble is considered this shows how the transient fluctuation relation asymptotically leads to the steady state relation when as explicitly checked in our systems the condition found in d j searles et al j stat phys 128 1337 2007 for the validity of the steady state fluctuation relation is verified for the steady state fluctuations of the phase space contraction rate and of the dissipation function a similar relaxation regime at shorter averaging times is found the quantity satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale the quantity appears to begin a monotonic convergence after such times this is consistent with the fact that and differ by a total time derivative and that the tails of the probability distribution function of are gaussian

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

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

sph simulations of time dependent poiseuille flow at low reynolds numbers a working smoothed particle hydrodynamics sph formalism for solving the equations of motion of a viscous fluid is presented the method is based on a standard symmetrized sph expression for the viscous forces which involves only first order derivatives of the kernel through a direct evaluation of the viscous stress tensor therefore the interpolation can be performed using low order kernels of compact support without compromising the accuracy and stability of the results in principle the scheme is suitable for treating compressible fluids with arbitrary shear and bulk viscosities here we demonstrate that when it is combined with the pressure gradient correction proposed by morris et al the method is also suitable for solving the navier stokes equations for incompressible flows without any further assumptions simulations using the method show close agreement with the analytic series solutions for plane poiseuille and hagen poiseuille flows at very low reynolds numbers at least for these specific tests the results obtained are essentially independent of employing either a cubic or a quintic spline kernel

time reversible continuum mechanics levesque and verlet developed a time reversible and bit reversible computational leapfrog algorithm their algorithm uses integer arithmetic and is exactly time reversible to the last computational bit describing the particle coordinates we generalize their idea developed for atomistic molecular dynamics to smoothed particle continuum mechanics in the special case of a two dimensional isentropic ideal gas these two approaches one microscopic and the other macroscopic are isomorphic in the more general nonadiabatic case but still without dissipative terms our continuum extension of the leapfrog scheme remains stable and also exhibits the exact time and bit reversibility associated with levesque and verlet s atomistic approach

thermodynamic entropy production fluctuation in a two dimensional shear flow model we investigate fluctuations in the momentum flux across a surface perpendicular to the velocity gradient in a stationary shear flow maintained by either thermostated deterministic or by stochastic boundary conditions in the deterministic system the fluctuation relation for the probability of large deviations which holds for the phase space volume contraction giving the gibbs ensemble entropy production never seems to hold for the flux which gives the hydrodynamic entropy production in the stochastic case the fluctuation relation is found to hold for the total flux as predicted by various exact results but not for the flux across part of the surface the latter appear to satisfy a modified fluctuation relation similar results are obtained for the heat flux in a steady state produced by stochastic boundaries at different temperatures

comparative evaluation of two superior stopping rules for hierarchical cluster analysis a split sample replication stopping rule for hierarchical cluster analysis is compared with the internal criterion previously found superior by milligan and cooper 1985 in their comparison of 30 different procedures the number and extent of overlap of the latent population distributions was systematically varied in the present evaluation of stopping rule validity equal and unequal population base rates were also considered both stopping rules correctly identified the actual number of populations when there was essentially no overlap and clusters occupied visually distinct regions of the measurement space the replication criterion which is evaluated by clustering of cluster means from preliminary analyses that are accomplished on random partitions of an original data set was superior as the degree of overlap in population distributions increased neither method performed adequately when overlap obliterated visually discernible density nodes

molecular dynamics and time reversibility we present a time symmetrical integer arithmetic algorithm for numerical molecular dynamics simulations of classical fluids this algorithm is used to illustrate through concrete examples that time asymmetric evolutions are typical for systems of many particles evolving according to reversible microscopic dynamics and to calculate the asymptotic behavior of the velocity autocorrelation function with an improved accuracy the equivalence between equilibrium time averages and microcanonical ensemble averages is checked via two new sampling methods for computing microcanonical averages of classical systems

curve counting and dt pt correspondence for calabi yau 4 folds abstract recently cao maulik toda defined stable pair invariants of a compact calabi yau 4 fold x their invariants are conjecturally related to the gopakumar vafa type invariants of x defined using gromov witten theory by klemm pandharipande in this paper we consider curve counting invariants of x using hilbert schemes of curves and conjecture a dt pt correspondence which relates these to stable pair invariants of x after providing evidence in the compact case we define analogous invariants for toric calabi yau 4 folds we formulate a vertex formalism for both theories and conjecture a relation between the fully equivariant dt pt vertex which we check in several cases this relation implies a dt pt correspondence for toric calabi yau 4 folds with primary insertions

comments on some aspects of boltzmann h theorem using reversible molecular dynamics we calculate the boltzmannh function for a repulsive lennard jones fluid using levesque and verlet s reversible molecular dynamics algorithm we find as predicted by jaynes that for certain initial states h increases as a function of time we also discuss the grad limit within such a simulation

fluctuation relation beyond linear response theory the fluctuation relation fr is an asymptotic result onthe distribution of certain observables averaged over timeintervals as and it is a generalization of thefluctuation dissipation theorem to far from equilibrium systemsin a steady state which reduces to the usual green kubo gk relation in the limit of small external non conservative forces fr is a theorem for smooth uniformly hyperbolic systems and it isassumed to be true in all dissipative chaotic enough systemsin a steady state in this paper we develop a theory of finitetime corrections to fr needed to compare the asymptoticprediction of fr with numerical observations which necessarilyinvolve fluctuations of observables averaged over finite timeintervals we perform a numerical test of fr in two cases inwhich non gaussian fluctuations are observable while gk does notapply and we get a non trivial verification of fr that is independent of and different from linear response theory our results are compatible with the theory of finite timecorrections to fr while fr would be observably violated well within the precision of our experiments if such correctionswere neglected

billiards correlation functions we discuss various experiments on the time decay of velocity autocorrelation functions in billiards we perform new experiments and find results which are compatible with an exponential mixing hypothesis first put forward by friedman and martin fm they do not seem compatible with the stretched exponentials believed in spite of fm and more recently of chernov to describe the mixing the analysis leads to several byproducts we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in timetm astm finding a strong dependence on some geometric characteristics of the locus of the billiard obstacles

conformally symplectic dynamics and symmetry of the lyapunov spectrum a generalization of the hamiltonian formalism is studied and the symmetry of the lyapunov spectrum established for the resulting systems the formalism is applied to the gausssian isokinetic dynamics of interacting particles with hard core collisions and other systems

reexamination of experimental tests of the fluctuation theorem the fluctuation theorem and the jarzynski equality are examined in the light of recent experimental tests for a particle dragged through a solvent it is shown that q the heat exchanged with the reservoir does not obey the jarzynski equality due to slowly decaying tails in its distribution for molecular stretching experiments substantial corrections to the jarzynski equality can result from not measuring the force at the end of the molecule that is moved we also present a proof of the fluctuation theorem for langevin dynamics that is considerably simpler than the standard proof

when can one observe good hydrodynamic lyapunov modes inspired by recent results on differences in fluctuations of finite time lyapunov exponents between hard core and soft potential systems we surmise that partial domination of the oseledec splitting dos with respect to subspaces associated with near zero lyapunov exponents is essential for observing good hydrodynamic lyapunov modes hlms numerical results for coupled map lattices are presented to show the importance of dos for observing good hlms this is achieved by relating splitting parameters to the maximum value of the lyapunov mode structure factor

temporal asymmetry of fluctuations in the nonequilibrium fpu model abstract the large deviation theory recently developed by bertini de sole gabrielli jona lasinio and landim is meant to extend the onsager machlup theory to nonequilibrium phenomena and predicts that the fluctuations of densities and currents in certain stochastic processes are not symmetric with respect to the time reversal operation in this paper several notions of fluctuations are introduced for deterministic systems and it is observed that temporally asymmetric not necessarily large fluctuations are ubiquitous even in the context of time reversal invariant dynamics of particle systems in nonequilibrium states to illustrate these ideas the nonequilibrium fpu chain devised by lepri livi and politi is studied in detail

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

an examination of procedures for determining the number of clusters in a data set a monte carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2 3 4 or 5 distinct nonoverlapping clusters to provide a variety of clustering solutions the data sets were analyzed by four hierarchical clustering methods external criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level thus the clustering present in the data was quite strong the simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data several procedures worked fairly well whereas others performed rather poorly thus the latter group of rules would appear to have little validity particularly for data sets containing distinct clusters applied researchers are urged to select one or more of the better criteria however users are cautioned that the performance of some of the criteria may be data dependent

orientability of moduli spaces of spin 7 instantons and coherent sheaves on calabi yau 4 folds abstract suppose x g is a compact spin 7 manifold e g a riemannian 8 manifold with holonomy spin 7 or a calabi yau 4 fold let g be u m or su m and p x be a principal g bundle we show that the infinite dimensional moduli space b p of all connections on p modulo gauge is orientable in a certain sense we deduce that the moduli space m p spin 7 b p of irreducible spin 7 instanton connections on p modulo gauge as a manifold or derived manifold is orientable this improves theorems of cao and leung 9 and munoz and shahbazi 42 if x is a calabi yau 4 fold the derived moduli stack m of complexes of coherent sheaves on x is a 2 shifted symplectic derived stack m by pantev toen vaquie vezzosi 46 and so has a notion of orientation by borisov joyce 7 we prove that m is orientable by relating algebro geometric orientations on m to differential geometric orientations on b p for u m bundles p x and using orientability of b p this has applications to defining donaldson thomas type invariants counting semistable coherent sheaves on a calabi yau 4 fold as in donaldson and thomas 15 cao and leung 8 and borisov and joyce 7

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

orientability for gauge theories on calabi yau manifolds abstract we study orientability issues of moduli spaces from gauge theories on calabi yau manifolds our results generalize and strengthen those for donaldson thomas theory on calabi yau manifolds of dimensions 3 and 4 we also prove a corresponding result in the relative situation which is relevant to the gluing formula in dt theory

entropy production fluctuations of finite markov chains for almost every trajectory segment over a finite time span of a finite markov chain with any given initial distribution the logarithm of the ratio of its probability to that of its time reversal converges exponentially to the entropy production rate of the markov chain the large deviation rate function has a symmetry of gallavotti cohen type which is called the fluctuation theorem moreover similar symmetries also hold for the rate functions of the joint distributions of general observables and the logarithmic probability ratio

the steady state fluctuation relation for the dissipation function we give a proof of transient fluctuation relations for the entropy production dissipation function in nonequilibrium systems which is valid for most time reversible dynamics we then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax producing a unique nonequilibrium steady state although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown if such a steady state exists the generation of the steady state fluctuation relation from the transient relation is shown to be very general it is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation which is needed also for e g the existence of transport coefficients because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities the steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor whose convergence is problematic for systems close to equilibrium we examine some model dynamics that have been considered previously and show how they are described in the context of this work

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

a cautionary note on using internal cross validation to select the number of clusters a highly popular method for examining the stability of a data clustering is to split the data into two parts cluster the observations in part a assign the objects in part b to their nearest centroid in part a and then independently cluster the part b objects one then examines how close the two partitions are say by the rand measure another proposal is to split the data into k parts and see how their centroids cluster by means of synthetic data analyses we demonstrate that these approaches fail to identify the appropriate number of clusters particularly as sample size becomes large and the variables exhibit higher correlations

microscopic origins of irreversible macroscopic behavior time asymmetric behavior as embodied in the second law of thermodynamics is observed in individual macroscopic systems it can be understood as arising naturally from time symmetric microscopic laws in accord with the ideas of thompson maxwell and boltzmann alternative explanations based on equating irreversible macroscopic behavior with the mixing type of behavior already present in the time evolution of ensembles probability distributions of certain systems having only a few degrees of freedom are in my opinion unnecessary misguided and misleading

gopakumar vafa type invariants on calabi yau 4 folds via descendent insertions the gopakumar vafa type invariants on calabi yau 4 folds which are non trivial only for genus zero and one are defined by klemm pandharipande from gromov witten theory and their integrality is conjectured in a previous work of cao maulik toda mathop mathrm dt nolimits 4 invariants with primary insertions on moduli spaces of one dimensional stable sheaves are used to give a sheaf theoretical interpretation of the genus zero gv type invariants in this paper we propose a sheaf theoretical interpretation of the genus one gv type invariants using descendent insertions on the above moduli spaces the conjectural formula in particular implies nontrivial constraints on genus zero gv type equivalently gw invariants of cy 4 folds which can be proved by the wdvv equation

chaotic principle some applications to developed turbulence some models for developed turbulence are considered they are shown to obey a large fluctuations theorem and one of them also obeys a response reciprocity relation of onsager type this illustrates and extends ideas and techniques developed in earlier works mainly for nonequilibrium problems in statistical mechanics

hamiltonian derivation of a detailed fluctuation theorem we analyze the microscopic evolution of a system undergoing a far from equilibrium thermodynamic process explicitly accounting for the degrees of freedom of participating heat reservoirs we derive a hybrid result similar in form to both the fluctuation theorem and a statement of detailed balance we relate this result to the steady state fluctuation theorem and to a free energy relation valid far from equilibrium

chaotic hypothesis fluctuation theorem and singularities the chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them however its application to physics problems requires attention and can lead to apparent inconsistencies in particular there are several cases that have been considered in the literature in which singularities are built in the models for instance when among the forces there are lennard jones potentials which are infinite in the origin and the constraints imposed on the system do not forbid arbitrarily close approach to the singularity even though the average kinetic energy is bounded the situation is well understood in certain special cases in which the system is subject to gaussian noise here the treatment of rather general singular systems is considered and the predictions of the chaotic hypothesis for such situations are derived the main conclusion is that the chaotic hypothesis is perfectly adequate to describe the singular physical systems we consider ie deterministic systems with thermostat forces acting according to gauss principle for the constraint of constant total kinetic energy isokinetic gaussian thermostats close and far from equilibrium near equilibrium it even predicts a fluctuation relation which in deterministic cases with more general thermostat forces ie not necessarily of gaussian isokinetic nature extends recent relations obtained in situations in which the thermostatting forces satisfy gauss principle this relation agrees where expected with the fluctuation theorem for perfectly chaotic systems the results are compared with some recent works in the literature

test of the fluctuation relation in lagrangian turbulence on a free surface the statistics of velocity divergence are studied for an assembly of particles that float on a closed turbulent fluid under an appropriate definition of entropy the two dimensional lagrangian velocity divergence of a particle trajectory represents the local entropy rate dot s a random variable in time the statistics of this rate measured in the lagrangian frame are collected over a wide range of values this permits a severe test of the fluctuation relation fr over a range that exceeds prior experiments out to a regime beyond which the fr no longer holds notably the probability density functions pdf of the dimensionless divergence are strongly non gaussian

time reversibility in nonequilibrium thermomechanics abstract time reversibility of dynamical systems has had many different interpretations for the governing differential equations for the numerical approximations to their solutions for the maps which caricature these equations and their solutions and for the phase space distributions describing ensembles of systems here i discuss some of these views taken from recent research literature and relate them to my own experience which is primarily computational i emphasize the usefulness of thermomechanics a simple generalization of conventional molecular dynamics which leads directly inexorably and paradoxically from hamilton s principle of least action to the multifractal time irreversible phase space behavior summed up by the macroscopic second law of thermodynamics

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

what symbolic dynamics do we get with a misplaced partition on the validity of threshold crossings analysis of chaotic time series abstract an increasingly popular method of encoding chaotic time series from physical experiments is the so called threshold crossings technique where one simply replaces the real valued data with symbolic data of relative positions to an arbitrary partition at discrete times the implication has been that this symbolic encoding describes the original dynamical system on the other hand the literature on generating partitions of non hyperbolic dynamical systems has shown that a good partition is non trivial to find it is believed that the generating partition of non uniformly hyperbolic dynamical system connects primary tangencies which are generally not simple lines as used by a threshold crossings therefore we investigate consequences of using itineraries generated by a non generating partition we do most of our rigorous analysis using the tent map as a benchmark example but show numerically that our results likely generalize in summary we find the misrepresentation of the dynamical system by sample path symbolic dynamics of an arbitrary partition can be severe including sometimes extremely diminished topological entropy and a high degree of non uniqueness interestingly we find topological entropy as a function of misplacement to be devil s staircase like but surprisingly non monotone

structure of characteristic lyapunov vectors in spatiotemporal chaos we study lyapunov vectors lvs corresponding to the largest lyapunov exponents in systems with spatiotemporal chaos we focus on characteristic lvs and compare the results with backward lvs obtained via successive gram schmidt orthonormalizations systems of a very different nature such as coupled map lattices and the continuous time lorenz 96 model exhibit the same features in quantitative and qualitative terms additionally we propose a minimal stochastic model that reproduces the results for chaotic systems our work supports the claims about universality of our earlier results i g szendro phys rev e 76 025202 r 2007 for a specific coupled map lattice

spatiotemporal structure of lyapunov vectors in chaotic coupled map lattices the spatiotemporal dynamics of lyapunov vectors lvs in spatially extended chaotic systems is studied by means of coupled map lattices we determine intrinsic length scales and spatiotemporal correlations of lvs corresponding to the leading unstable directions by translating the problem to the language of scale invariant growing surfaces we find that the so called characteristic lvs exhibit spatial localization strong clustering around given spatiotemporal loci and remarkable dynamic scaling properties of the corresponding surfaces in contrast the commonly used backward lvs obtained through gram schmidt orthogonalization spread all over the system and do not exhibit dynamic scaling due to artifacts in the dynamical correlations by construction

on the definition of entropy production via examples we present a definition of entropy production rate for classes of deterministic and stochastic dynamics the point of departure is a gibbsian representation of the steady state path space measure for which the density is determined with respect to the time reversed process the gibbs formalism is used as a unifying algorithm capable of incorporating basic properties of entropy production in nonequilibrium systems our definition is motivated by recent work on the gallavotti cohen local fluctuation theorem and it is illustrated via a number of examples