Statistical optimization for passive scalar transport: maximum entropy production vs maximum Kolmogorov-Sinay entropy

Auteurs : Martin Mihelich, Berengere Dubrulle, Didier Paillard, Davide Faranda

arXiv: 1505.06861v1 - DOI (cond-mat.stat-mech)
Soumis à arXiv le 26 Mai. 2015
Résumé scientifique

We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov-Sinai entropy using a Markov model of the passive scalar diffusion called the Zero Range Process. We show analytically that both the entropy production and the Kolmogorov-Sinai entropy seen as functions of f admit a unique maximum denoted fmaxEP and fmaxKS. The behavior of these two maxima is explored as a function of the system disequilibrium and the system resolution N. The main result of this article is that fmaxEP and fmaxKS have the same Taylor expansion at _rst order in the deviation of equilibrium. We find that fmaxEP hardly depends on N whereas fmaxKS depends strongly on N. In particular, for a fixed difference of potential between the reservoirs, fmaxEP (N) tends towards a non-zero value, while fmaxKS (N) tends to 0 when N goes to infinity. For values of N typical of that adopted by Paltridge and climatologists we show that fmaxEP and fmaxKS coincide even far from equilibrium. Finally, we show that one can find an optimal resolution N_ such that fmaxEP and fmaxKS coincide, at least up to a second order parameter proportional to the non-equilibrium uxes imposed to the boundaries.

Les articles autour de lui, par date et par proximité

Plus haut, c’est plus proche de cet article ; à gauche, c’est plus ancien. Les traits relient les articles proches entre eux : les groupes de traits sont des sous-thèmes. Sélectionnez un point pour voir pourquoi il est là. Retour au résumé de cet article

Les articles les plus proches Les travaux antérieurs sur lesquels il s’appuie Les articles qui le citent

Les articles autour de celui-ci

Classés selon la proximité de leur titre et de leur résumé avec ceux de cet article. Sélectionnez-en pour les lire ensemble.

Les articles les plus proches

  1. Proche
    Maximum Kolmogorov-Sinai entropy vs minimum mixing time in Markov chains
    Martin Mihelich, Berengere Dubrulle, Didier Paillard et al. · 2015 · Mécanique statistique · Résumé IA disponible
    Résumé scientifique

    Many modern techniques employed in physics, such a computation of path integrals, rely on random walks on graphs that can be represented as Markov chains. Traditionally, estimates of running times of such sampling algorithms are computed using the number of steps in the chain needed to reach the stationary distribution. This quantity is generally defined as mixing time and is often difficult to compute. In this paper, we suggest an alternative estimate based on the Kolmogorov-Sinai entropy, by establishing a link between the maximization of KSE and the minimization of the mixing time. Since KSE are easier to compute in general than mixing time, this link provides a new faster method to appro…

  2. Apparenté
    Dissipation in Hydrodynamics from Micro- to Macroscale: Wisdom from Boltzmann and Stochastic Thermodynamics
    Danilo Forastiere, Francesco Avanzini, Massimiliano Esposito · 2023 · Mécanique statistique · Résumé IA disponible
    Résumé scientifique

    We show that macroscopic irreversible thermodynamics for viscous fluids can be derived from exact information-theoretic thermodynamic identities valid at the microscale. Entropy production in particular is a measure of the loss of many-particle correlations in the same way in which it measures the loss of system-reservoirs correlations in stochastic thermodynamics (ST). More specifically, we first show that boundary conditions at the macroscopic level define a natural decomposition of the entropy production rate (EPR) in terms of thermodynamic forces multiplying their conjugated currents, as well as a change in suitable nonequilibrium potential that acts as a Lyapunov function in absence of …

  3. Apparenté
    Tsallis nonextensive statistical mechanics of El Nino Southern Oscillation Index
    M. Ausloos, F. Petroni · 2006 · Physica A 373 (2007) 721 - 736 · Résumé IA disponible
    Résumé scientifique

    The shape and tails of partial distribution functions (PDF) for a climatological signal, i.e. the El Nino SOI and the turbulent nature of the ocean-atmosphere variability are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of the normalized variability for such a climatological index, for small and large time windows, both for small and large variability. This normalized variabil- ity distributions can be sufficiently well fitted with a chi-square-distribution. The transition between the smal…

  4. Apparenté
    Drift-Controlled Anomalous Diffusion: A Solvable Gaussian Model
    Fabrizio Lillo, Rosario N. Mantegna · 2000 · Mécanique statistique · Résumé IA disponible
    Résumé scientifique

    We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In particular diffusive, subdiffusive, superdiffusive and stretched exponentially diffusive processes are described by this model for specific values of the two control parameters. The model is also investigated in the presence of an external harmonic potential. We prove that the relaxation to the stationary solution is power-law in time with an exponent controlled by one of model parameters.

  5. Apparenté
    Continuously varying exponents in the distribution of waiting times in the symmetric exclusion process on a percolation cluster
    Arpan Chatterjee, Kabir Ramola, Deepak Dhar · 2026 · Mécanique statistique · Pas encore résumé
    Résumé scientifique

    We study the waiting-time distribution of hard-core interacting particles in the symmetric exclusion process on one- and two-dimensional lattices with side branches attached to each lattice site in the steady state. We use numerical simulations together with an approximate analytical treatment of particles trapped in side branches in the steady state. Such a two-dimensional carpet serves as a simplified model for trapping of a supercritical percolation cluster. At high particle densities, the system exhibits strong dynamical heterogeneity, with the distribution of logarithms of waiting times developing well-separated peaks corresponding to particles trapped at different depths from the backb…

  6. Apparenté
    Large deviation full counting statistics in adiabatic open quantum dynamics
    Paulo J. Paulino, Igor Lesanovsky, Federico Carollo · 2024 · Mécanique statistique · Résumé IA disponible
    Résumé scientifique

    The state of an open quantum system undergoing an adiabatic process evolves by following the instantaneous stationary state of its time-dependent generator. This observation allows one to characterize, for a generic adiabatic evolution, the average dynamics of the open system. However, information about fluctuations of dynamical observables, such as the number of photons emitted or the time-integrated stochastic entropy production in single experimental runs, requires controlling the whole spectrum of the generator and not only the stationary state. Here, we show how such information can be obtained in adiabatic open quantum dynamics by exploiting tools from large deviation theory. We prove …

  7. Apparenté
    Diffusion and Relaxation Controlled by Tempered α-stable Processes
    Aleksander Stanislavsky, Karina Weron, Aleksander Weron · 2011 · Phys. Rev. E 78, 051106 (2008) · Résumé IA disponible
    Résumé scientifique

    We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random operational time \tau. The tempering results in the existence of all moments of \tau. The subordination by the inverse tempered \alpha-stable process provides diffusion(relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation, the mean square displacement and the relaxation function. This model includes subdiffusion as a particular case…

  8. Apparenté
    Information Benchmark for Biological Sensors Beyond Steady States -- Mpemba-like sensory withdrawal effect
    Asawari Pagare, Zhiyue Lu · 2024 · Mécanique statistique · Résumé IA disponible
    Résumé scientifique

    Biological sensors rely on the temporal dynamics of ligand concentration for signaling. The sensory performance is bounded by the distinguishability between the sensory state transition dynamics under different environmental protocols. This work presents a comprehensive theory to characterize arbitrary transient sensory dynamics of biological sensors. Here the sensory performance is quantified by the Kullback-Leibler (KL) divergence between the probability distributions of the sensor's stochastic paths. We introduce a novel benchmark to assess a sensor's transient sensory performance arbitrarily far from equilibrium. We identify a counter-intuitive phenomenon in multi-state sensors: while an…

Comment ces articles sont-ils trouvés ?

Nous comparons le titre et le résumé de cet article avec ceux de tous les articles résumés sur ce site, et avec les articles que Semantic Scholar recommande, ceux qu’il cite et ceux qui le citent (pour un article très cité, ses citations les plus récentes et, depuis OpenAlex, les plus citées). Parmi les travaux antérieurs et les suites, les articles qui s’utilisent en profondeur, une méthode qu’il utilise et les suites très citées remontent un peu. Les niveaux (très proche, proche, apparenté) viennent de la similarité des textes, pas d’un jugement de qualité ; * signale un article sans résumé, comparé par son titre. La phrase sous un article est écrite par une IA à partir des deux résumés : vérifiez-la dans les articles. Un article jugé hors sujet par trois lecteurs quitte la liste.

Pour l’instant seulement parmi les articles résumés sur ce site : relancez la recherche pour ajouter les travaux antérieurs, les suites et les recommandations de Semantic Scholar.