898 research outputs found
Law without law or "just" limit theorems?
About 35 years ago Wheeler introduced the motto `law without law' to
highlight the possibility that (at least a part of) Physics may be understood
only following {\em regularity principles} and few relevant facts, rather than
relying on a treatment in terms of fundamental theories. Such a proposal can be
seen as part of a more general attempt (including the maximum entropy approach)
summarized by the slogan `it from bit', which privileges the information as the
basic ingredient. Apparently it seems that it is possible to obtain, without
the use of physical laws, some important results in an easy way, for instance,
the probability distribution of the canonical ensemble. In this paper we will
present a general discussion on those ideas of Wheeler's that originated the
motto `law without law'. In particular we will show how the claimed simplicity
is only apparent and it is rather easy to produce wrong results. We will show
that it is possible to obtain some of the results treated by Wheeler in the
realm of the statistical mechanics, using precise assumptions and nontrivial
results of probability theory, mainly concerning ergodicity and limit theorems.Comment: 9 pages, 3 figure
Compressibility, laws of nature, initial conditions and complexity
We critically analyse the point of view for which laws of nature are just a
mean to compress data. Discussing some basic notions of dynamical systems and
information theory, we show that the idea that the analysis of large amount of
data by means of an algorithm of compression is equivalent to the knowledge one
can have from scientific laws, is rather naive. In particular we discuss the
subtle conceptual topic of the initial conditions of phenomena which are
generally incompressible. Starting from this point, we argue that laws of
nature represent more than a pure compression of data, and that the
availability of large amount of data, in general, is not particularly useful to
understand the behaviour of complex phenomena.Comment: 19 Pages, No figures, published on Foundation of Physic
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
Efficiency of a stirred chemical reaction in a closed vessel
We perform a numerical study of the reaction efficiency in a closed vessel.
Starting with a little spot of product, we compute the time needed to complete
the reaction in the container following an advection-reaction-diffusion
process. Inside the vessel it is present a cellular velocity field that
transports the reactants. If the size of the container is not very large
compared with the typical length of the velocity field one has a plateau of the
reaction time as a function of the strength of the velocity field, . This
plateau appears both in the stationary and in the time-dependent flow. A
comparison of the results for the finite system with the infinite case (for
which the front speed, , gives a simple estimate of the reacting time)
shows the dramatic effect of the finite size.Comment: 4 pages, 4 figure
Multiple-scale analysis and renormalization for pre-asymptotic scalar transport
Pre-asymptotic transport of a scalar quantity passively advected by a
velocity field formed by a large-scale component superimposed to a small-scale
fluctuation is investigated both analytically and by means of numerical
simulations. Exploiting the multiple-scale expansion one arrives at a
Fokker--Planck equation which describes the pre-asymptotic scalar dynamics.
Such equation is associated to a Langevin equation involving a multiplicative
noise and an effective (compressible) drift. For the general case, no explicit
expression for both the effective drift and the effective diffusivity (actually
a tensorial field) can be obtained. We discuss an approximation under which an
explicit expression for the diffusivity (and thus for the drift) can be
obtained. Its expression permits to highlight the important fact that the
diffusivity explicitly depends on the large-scale advecting velocity. Finally,
the robustness of the aforementioned approximation is checked numerically by
means of direct numerical simulations.Comment: revtex4, 12 twocolumn pages, 3 eps figure
Introduction to chaos and diffusion
This contribution is relative to the opening lectures of the ISSAOS 2001
summer school and it has the aim to provide the reader with some concepts and
techniques concerning chaotic dynamics and transport processes in fluids. Our
intention is twofold: to give a self-consistent introduction to chaos and
diffusion, and to offer a guide for the reading of the rest of this volume.Comment: 39 page
About the role of chaos and coarse graining in Statistical Mechanics
We discuss the role of ergodicity and chaos for the validity of statistical
laws. In particular we explore the basic aspects of chaotic systems (with
emphasis on the finite-resolution) on systems composed of a huge number of
particles.Comment: Summer school `Fundamental Problems in Statistical Physics' (Leuven,
Belgium), June 16-29, 2013. To be published in Physica
Linear and anomalous front propagation in system with non Gaussian diffusion: the importance of tails
We investigate front propagation in systems with diffusive and sub-diffusive
behavior. The scaling behavior of moments of the diffusive problem, both in the
standard and in the anomalous cases, is not enough to determine the features of
the reactive front. In fact, the shape of the bulk of the probability
distribution of the transport process, which determines the diffusive
properties, is important just for pre-asymptotic behavior of front propagation,
while the precise shape of the tails of the probability distribution determines
asymptotic behavior of front propagation.Comment: 7 pages, 3 figure
Linear and non-linear thermodynamics of a kinetic heat engine with fast transformations
We investigate a kinetic heat engine model constituted by particles enclosed
in a box where one side acts as a thermostat and the opposite side is a piston
exerting a given pressure. Pressure and temperature are varied in a cyclical
protocol of period : their relative excursions, and
respectively, constitute the thermodynamic forces dragging the system
out-of-equilibrium. The analysis of the entropy production of the system allows
to define the conjugated fluxes, which are proportional to the extracted work
and the consumed heat. In the limit of small and the fluxes
are linear in the forces through a -dependent Onsager matrix whose
off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston
can be approximated, through a coarse-graining procedure, by a Klein-Kramers
equation which - in the linear regime - yields analytic expressions for the
Onsager coefficients and the entropy production. A study of the efficiency at
maximum power shows that the Curzon-Ahlborn formula is always an upper limit
which is approached at increasing values of the thermodynamic forces, i.e.
outside of the linear regime. In all our analysis the adiabatic limit and the the small force limit are not directly
related.Comment: 10 pages, 9 figure
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