Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy decay for the Kac evolution   We consider solutions to the Kac master equation for initial conditions where
$N$ particles are in a thermal equilibrium and $M\le N$ particles are out of
equilibrium. We show that such solutions have exponential decay in entropy
relative to the thermal state. More precisely, the decay is exponential in time
with an explicit rate that is essentially independent on the particle number.
This is in marked contrast to previous results which show that the entropy
production for arbitrary initial conditions is inversely proportional to the
particle number. The proof relies on Nelson's hypercontractive estimate and the
geometric form of the Brascamp-Lieb inequalities due to Franck Barthe. Similar
results hold for the Kac-Boltzmann equation with uniform scattering cross
sections.

17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph