Artículos con la etiqueta ‘Statistical Mechanics (cond-mat.stat-mech)’

Entropy is in Flux

Por • 30 mar, 2014 • Category: Crítica

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium ones. However, starting with the work of Ludwig Boltzmann in 1872, and continuing to the present day, various models of non-equilibrium behavior have been put together with the specific aim of generalizing the concept of entropy to non-equilibrium situations. This kind of entropy has been termed {\em kinetic entropy} to distinguish it from the thermodynamic variety. Knowledge of kinetic entropy started from Boltzmann’s insight about his equation for the time dependence of gaseous systems. In this paper, his result is stated as a definition of kinetic entropy in terms of a local equation for the entropy density. This definition is then applied to Landau’s theory of the Fermi liquid thereby giving the kinetic entropy within that theory.

Innovations in Statistical Physics

Por • 29 mar, 2014 • Category: Leyes

In 1963-71, a group of people, myself included, formulated and perfected a new approach to physics problems, which eventually came to be known under the names of scaling, universality, and renormalization. This work formed the basis of a wide variety of theories ranging from its starting point in critical phenomena, and moving out to particle physics and relativity and then into economics and biology. This work was of transcendental beauty and of considerable intellectual importance.

Thermodynamical Phase transitions, the mean-field theories, and the renormalization (semi)group: A pedagogical introduction

Por • 1 mar, 2014 • Category: Leyes

Mean field theories are good qualitative descriptors of the phase transition behavior. But all mean-field theories (including Landau’s theory) fail at the critical point (the problem of large correlation length). The problems with large correlation length in quantum many-body systems are the hardest problems known in theoretical physics (both in condensed matter and in particle physics). It was Ken Wilson’s physical insights and his powerful mathematical skills that opened a way to the solution of such hard problems. This manuscript is a perspective on these issues. Starting with simple examples of phase transitions (like ice/water; diamond/graphite etc.) we address the following important questions: Why does non-analyticity (sharp phase transitions) arise when thermodynamical functions (i.e., free energies etc) are good analytic functions? How does Landau’s program unify all the previous mean-field theories? Why do all the mean-field theories fail near the critical point? How does Wilson’s program go beyond all the mean-field theories? What is the origin emergence and universality?

Wilson’s renormalization group: a paradigmatic shift

Por • 17 feb, 2014 • Category: Leyes

A personal and subjective recollection, concerning mainly Wilson’s lectures delivered over the spring of 1972 at Princeton University (summary of a talk at Cornell University on November 16, 2013 at the occasion of the memorial Kenneth G. Wilson conference).

Is ergodicity a reasonable hypothesis?

Por • 30 ene, 2014 • Category: Leyes

In the physics literature «ergodicity» is taken to mean that a system, including a macroscopic one, visits all microscopic states in a relatively short time. We show that this is an impossibility even if that time is billions of years. We also suggest that this feature does not contradict most physical considerations since those considerations deal with correlations of only a few particles.

Chaos Forgets and Remembers: Measuring Information Creation, Destruction, and Storage

Por • 1 oct, 2013 • Category: Filosofía

The hallmark of deterministic chaos is that it creates information—the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a system’s intrinsic unpredictability. Here, we show that it naturally decomposes into two structurally meaningful components: A portion of the created information—the ephemeral information—is forgotten and a portion—the bound information—is remembered. The bound information is a new kind of intrinsic computation that differs fundamentally from information creation: it measures the rate of active information storage. We show that it can be directly and accurately calculated via symbolic dynamics, revealing a hitherto unknown richness in how dynamical systems compute.

The Legacy of Ken Wilson

Por • 11 ago, 2013 • Category: Ambiente

This is a brief account of the legacy of Ken Wilson in statistical physics, high energy physics, computing and education.

Statistical Mechanics of Competitive Resource Allocation

Por • 13 may, 2013 • Category: Economía

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines.

Evolution in a Changing Environment

Por • 24 abr, 2013 • Category: Ambiente

We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with «specialist» individuals that are adapted to the environment; this maximum moves over time as the environment changes. The other maximum is static, and represents «generalist» individuals not affected by environmental changes. The rest of the landscape is occupied by «maladapted» individuals. Our analysis considers the evolution of these three subpopulations. Our main result is that, in presence of a sufficiently stable environmental feature, as in the case of an unchanging aspect of a physical habitat, specialists can dominate the population. By contrast, rapidly changing environmental features, such as language or cultural habits, are a moving target for the genes; here, generalists dominate, because the best evolutionary strategy is to adopt neutral alleles not specialized for any specific environment. The model we propose is based on simple assumptions about evolutionary dynamics and describes all possible scenarios in a non-trivial phase diagram. The approach provides a general framework to address such fundamental issues as the Baldwin effect, the biological basis for language, or the ecological consequences of a rapid climate change.

Editorial: Statistical Mechanics and Social Sciences

Por • 6 abr, 2013 • Category: Economía

This editorial opens the special issues that the Journal of Statistical Physics has dedicated to the growing field of statistical physics modeling of social dynamics. The issues include contributions from physicists and social scientists, with the goal of fostering a better communication between these two communities. The contents of the special issue can be found at these links: this http URL (Volume I) and this http URL (Volume II)