Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Celebrating Cercignani's conjecture for the Boltzmann equation   Cercignani's conjecture assumes a linear inequality between the entropy and
entropy production functionals for Boltzmann's nonlinear integral operator in
rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities
and spectral gap inequalities, this issue has been at the core of the renewal
of the mathematical theory of convergence to thermodynamical equilibrium for
rarefied gases over the past decade. In this review paper, we survey the
various positive and negative results which were obtained since the conjecture
was proposed in the 1980s.

21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an