Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New treatments of density fluctuations and recurrence times for
  re-estimating Zermelo's paradox   What is the probability that all the gas in a box accumulates in the same
half of this box? Though amusing, this question underlies the fundamental
problem of density fluctuations at equilibrium, which has profound
implementations in many physical fields. The currently accepted solutions are
derived from the studies of Brownian motion by Smoluchowski, but they are not
appropriate for the directly colliding particles of gases. Two alternative
theories are proposed here using self-regulatory Bernoulli distributions. A
discretization of space is first introduced to develop a mechanism of matter
congestion holding for high densities. In a second mechanism valid in ordinary
conditions, the influence of local pressure on the location of every particle
is examined using classical laws of ideal gases. This approach reveals that a
negative feedback results from the reciprocal influences between individual
particles and the population of particles, which strongly reduces the
probability of atypical microstates. Finally, a thermodynamic quantum of time
is defined to compare the recurrence times of improbable macrostates predicted
through these different approaches.

3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc