35,678 research outputs found
Temperature in and out of equilibrium: a review of concepts, tools and attempts
We review the general aspects of the concept of temperature in equilibrium
and non-equilibrium statistical mechanics. Although temperature is an old and
well-established notion, it still presents controversial facets. After a short
historical survey of the key role of temperature in thermodynamics and
statistical mechanics, we tackle a series of issues which have been recently
reconsidered. In particular, we discuss different definitions and their
relevance for energy fluctuations. The interest in such a topic has been
triggered by the recent observation of negative temperatures in condensed
matter experiments. Moreover, the ability to manipulate systems at the micro
and nano-scale urges to understand and clarify some aspects related to the
statistical properties of small systems (as the issue of temperature's
"fluctuations"). We also discuss the notion of temperature in a dynamical
context, within the theory of linear response for Hamiltonian systems at
equilibrium and stochastic models with detailed balance, and the generalised
fluctuation-response relations, which provide a hint for an extension of the
definition of temperature in far-from-equilibrium systems. To conclude we
consider non-Hamiltonian systems, such as granular materials, turbulence and
active matter, where a general theoretical framework is still lacking.Comment: Review article, 137 pages, 12 figure
Brownian motion: a paradigm of soft matter and biological physics
This is a pedagogical introduction to Brownian motion on the occasion of the
100th anniversary of Einstein's 1905 paper on the subject. After briefly
reviewing Einstein's work in its contemporary context, we pursue some lines of
further developments and applications in soft condensed matter and biology.
Over the last century Brownian motion became promoted from an odd curiosity of
marginal scientific interest to a guiding theme pervading all of the modern
(live) sciences.Comment: 30 pages, revie
A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
In this work it is shown how the immersed boundary method of (Peskin2002) for
modeling flexible structures immersed in a fluid can be extended to include
thermal fluctuations. A stochastic numerical method is proposed which deals
with stiffness in the system of equations by handling systematically the
statistical contributions of the fastest dynamics of the fluid and immersed
structures over long time steps. An important feature of the numerical method
is that time steps can be taken in which the degrees of freedom of the fluid
are completely underresolved, partially resolved, or fully resolved while
retaining a good level of accuracy. Error estimates in each of these regimes
are given for the method. A number of theoretical and numerical checks are
furthermore performed to assess its physical fidelity. For a conservative
force, the method is found to simulate particles with the correct Boltzmann
equilibrium statistics. It is shown in three dimensions that the diffusion of
immersed particles simulated with the method has the correct scaling in the
physical parameters. The method is also shown to reproduce a well-known
hydrodynamic effect of a Brownian particle in which the velocity
autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times.
A few preliminary results are presented for more complex systems which
demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic
Field-theoretic methods
Many complex systems are characterized by intriguing spatio-temporal
structures. Their mathematical description relies on the analysis of
appropriate correlation functions. Functional integral techniques provide a
unifying formalism that facilitates the computation of such correlation
functions and moments, and furthermore allows a systematic development of
perturbation expansions and other useful approximative schemes. It is explained
how nonlinear stochastic processes may be mapped onto exponential probability
distributions, whose weights are determined by continuum field theory actions.
Such mappings are madeexplicit for (1) stochastic interacting particle systems
whose kinetics is defined through a microscopic master equation; and (2)
nonlinear Langevin stochastic differential equations which provide a mesoscopic
description wherein a separation of time scales between the relevant degrees of
freedom and background statistical noise is assumed. Several well-studied
examples are introduced to illustrate the general methodology.Comment: Article for the Encyclopedia of Complexity and System Science, B.
Meyers (Ed.), Springer-Verlag Berlin, 200
Long-range correlations in non-equilibrium systems: Lattice gas automaton approach
In systems removed from equilibrium, intrinsic microscopic fluctuations
become correlated over distances comparable to the characteristic macroscopic
length over which the external constraint is exerted. In order to investigate
this phenomenon, we construct a microscopic model with simple stochastic
dynamics using lattice gas automaton rules that satisfy local detailed balance.
Because of the simplicity of the automaton dynamics, analytical theory can be
developed to describe the space and time evolution of the density fluctuations.
The exact equations for the pair correlations are solved explicitly in the
hydrodynamic limit. In this limit, we rigorously derive the results obtained
phenomenologically by fluctuating hydrodynamics. In particular, the spatial
algebraic decay of the equal-time fluctuation correlations predicted by this
theory is found to be in excellent agreement with the results of our lattice
gas automaton simulations for two different types of boundary conditions.
Long-range correlations of the type described here appear generically in
dynamical systems that exhibit large scale anisotropy and lack detailed
balance.Comment: 23 pages, RevTeX; to appear in Phys. Rev.
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