2 research outputs found
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
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