6 research outputs found
Entropy production and coarse-graining in Markov processes
We study the large time fluctuations of entropy production in Markov
processes. In particular, we consider the effect of a coarse-graining procedure
which decimates {\em fast states} with respect to a given time threshold. Our
results provide strong evidence that entropy production is not directly
affected by this decimation, provided that it does not entirely remove loops
carrying a net probability current. After the study of some examples of random
walks on simple graphs, we apply our analysis to a network model for the
kinesin cycle, which is an important biomolecular motor. A tentative general
theory of these facts, based on Schnakenberg's network theory, is proposed.Comment: 18 pages, 13 figures, submitted for publicatio
Entropy production and coarse-graining in Markov processes
We study the large time fluctuations of entropy production in Markov
processes. In particular, we consider the effect of a coarse-graining procedure
which decimates {\em fast states} with respect to a given time threshold. Our
results provide strong evidence that entropy production is not directly
affected by this decimation, provided that it does not entirely remove loops
carrying a net probability current. After the study of some examples of random
walks on simple graphs, we apply our analysis to a network model for the
kinesin cycle, which is an important biomolecular motor. A tentative general
theory of these facts, based on Schnakenberg's network theory, is proposed.Comment: 18 pages, 13 figures, submitted for publicatio
Coarse-Grained Probabilistic Automata Mimicking Chaotic Systems
Discretization of phase space usually nullifies chaos in dynamical systems.
We show that if randomness is associated with discretization dynamical chaos
may survive and be indistinguishable from that of the original chaotic system,
when an entropic, coarse-grained analysis is performed. Relevance of this
phenomenon to the problem of quantum chaos is discussed.Comment: 4 pages, 4 figure
Boltzmann entropy and chaos in a large assembly of weakly interacting systems
We introduce a high dimensional symplectic map, modeling a large system
consisting of weakly interacting chaotic subsystems, as a toy model to analyze
the interplay between single-particle chaotic dynamics and particles
interactions in thermodynamic systems. We study the growth with time of the
Boltzmann entropy, S_B, in this system as a function of the coarse graining
resolution. We show that a characteristic scale emerges, and that the behavior
of S_B vs t, at variance with the Gibbs entropy, does not depend on the coarse
graining resolution, as far as it is finer than this scale. The interaction
among particles is crucial to achieve this result, while the rate of entropy
growth depends essentially on the single-particle chaotic dynamics (for t not
too small). It is possible to interpret the basic features of the dynamics in
terms of a suitable Markov approximation.Comment: 21 pages, 11 figures, submitted to Journal of Statistical Physic
Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space
We show that an appropriate description of the non-equilibrium dynamics of
disordered systems is obtained through a strong disorder renormalization
procedure in {\it configuration space}, that we define for any master equation
with transitions rates between configurations. The
idea is to eliminate iteratively the configuration with the highest exit rate
to obtain
renormalized transition rates between the remaining configurations. The
multiplicative structure of the new generated transition rates suggests that,
for a very broad class of disordered systems, the distribution of renormalized
exit barriers defined as
will become broader and broader upon iteration, so that the strong disorder
renormalization procedure should become asymptotically exact at large time
scales. We have checked numerically this scenario for the non-equilibrium
dynamics of a directed polymer in a two dimensional random medium.Comment: v2=final versio
Artificial Sequences and Complexity Measures
In this paper we exploit concepts of information theory to address the
fundamental problem of identifying and defining the most suitable tools to
extract, in a automatic and agnostic way, information from a generic string of
characters. We introduce in particular a class of methods which use in a
crucial way data compression techniques in order to define a measure of
remoteness and distance between pairs of sequences of characters (e.g. texts)
based on their relative information content. We also discuss in detail how
specific features of data compression techniques could be used to introduce the
notion of dictionary of a given sequence and of Artificial Text and we show how
these new tools can be used for information extraction purposes. We point out
the versatility and generality of our method that applies to any kind of
corpora of character strings independently of the type of coding behind them.
We consider as a case study linguistic motivated problems and we present
results for automatic language recognition, authorship attribution and self
consistent-classification.Comment: Revised version, with major changes, of previous "Data Compression
approach to Information Extraction and Classification" by A. Baronchelli and
V. Loreto. 15 pages; 5 figure