Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: math
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex