857 research outputs found

### Fluctuation Theorem and Chaos

The heat theorem (i.e. the second law of thermodynamics or the existence of
entropy) is a manifestation of a general property of hamiltonian mechanics and
of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary
states the chaotic hypothesis plays a similar role: it allows a unique
determination of the probability distribution (called {\rm SRB} distribution on
phase space providing the time averages of the observables. It also implies an
expression for a few averages concrete enough to derive consequences of
symmetry properties like the fluctuation theorem or to formulate a theory of
coarse graining unifying the foundations of equilibrium and of nonequilibrium.Comment: Basis for the plenary talk at StatPhys23 (Genova July 2007

### Borel summability and Lindstedt series

Resonant motions of integrable systems subject to perturbations may continue
to exist and to cover surfaces with parametric equations admitting a formal
power expansion in the strength of the perturbation. Such series may be,
sometimes, summed via suitable sum rules defining $C^\infty$ functions of the
perturbation strength: here we find sufficient conditions for the Borel
summability of their sums in the case of two-dimensional rotation vectors with
Diophantine exponent $\tau=1$ (e. g. with ratio of the two independent
frequencies equal to the golden mean).Comment: 17 pages, 1 figur

### Reversible viscosity and Navier--Stokes fluids

Exploring the possibility of describing a fluid flow via a time-reversible
equation and its relevance for the fluctuations statistics in stationary
turbulent (or laminar) incompressible Navier-Stokes flows.Comment: 7 pages 6 figures, v2: replaced Fig.6 and few changes. Last version:
appendix cut shorter, because of a computational erro

### Entropy, Thermostats and Chaotic Hypothesis

The chaotic hypothesis is proposed as a basis for a general theory of
nonequilibrium stationary states.
Version 2: new comments added after presenting this talk at the Meeting
mentioned in the Acknowledgement. One typo corrected.Comment: 6 page

### Non equilibrium in statistical and fluid mechanics. Ensembles and their equivalence. Entropy driven intermittency

We present a review of the chaotic hypothesis and discuss its applications to
intermittency in statistical mechanics and fluid mechanics proposing a
quantitative definition. Entropy creation rate is interpreted in terms of
certain intermittency phenomena. An attempt to a theory of the experiment of
Ciliberto-Laroche on the fluctuation law is presented.Comment: 22 page

### Irreversibility time scale

Entropy creation rate is introduced for a system interacting with thermostats
({\it i.e.}, in the usual language, for a system subject to internal
conservative forces interacting with ``external'' thermostats via conservative
forces) and a fluctuation theorem for it is proved. As an application a time
scale is introduced, to be interpreted as the time over which irreversibility
becomes manifest in a process leading from an initial to a final stationary
state of a mechanical system in a general nonequilibrium context. The time
scale is evaluated in a few examples, including the classical Joule-Thompson
process (gas expansion in a vacuum).
The new version (n.2) contains several comments on references pointed out to
me after posting the version n.1.Comment: 6 pages 1 figur

### A fluctuation theorem in a random environment

A simple class of chaotic systems in a random environment is considered and
the fluctuation theorem is extended under the assumption of reversibility.Comment: 9 page

### Note on nonequilibrium stationary states and entropy

In transformations between nonequilibrium stationary states, entropy might be
a not well defined concept. It might be analogous to the ``heat content'' in
transformations in equilibrium which is not well defined either, if they are
not isochoric ({\it i.e.} do involve mechanical work). Hence we conjecture that
un a nonequilbrium stationary state the entropy is just a quantity that can be
transferred or created, like heat in equilibrium, but has no physical meaning
as ``entropy content'' as a property of the system.Comment: 4 page

### Chaotic Hypothesis, Fluctuation Theorem and singularities

The chaotic hypothesis has several implications which have generated interest
in the literature because of their generality and because a few exact
predictions are among them. However its application to Physics problems
requires attention and can lead to apparent inconsistencies. In particular
there are several cases that have been considered in the literature in which
singularities are built in the models: for instance when among the forces there
are Lennard-Jones potentials (which are infinite in the origin) and the
constraints imposed on the system do not forbid arbitrarily close approach to
the singularity even though the average kinetic energy is bounded. The
situation is well understood in certain special cases in which the system is
subject to Gaussian noise; here the treatment of rather general singular
systems is considered and the predictions of the chaotic hypothesis for such
situations are derived. The main conclusion is that the chaotic hypothesis is
perfectly adequate to describe the singular physical systems we consider, i.e.
deterministic systems with thermostat forces acting according to Gauss'
principle for the constraint of constant total kinetic energy (``isokinetic
Gaussian thermostats''), close and far from equilibrium. Near equilibrium it
even predicts a fluctuation relation which, in deterministic cases with more
general thermostat forces (i.e. not necessarily of Gaussian isokinetic nature),
extends recent relations obtained in situations in which the thermostatting
forces satisfy Gauss' principle. This relation agrees, where expected, with the
fluctuation theorem for perfectly chaotic systems. The results are compared
with some recent works in the literature.Comment: 7 pages, 1 figure; updated to take into account comments received on
the first versio

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