Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tipping of a classical point mass pendulum: Role of statistical
  fluctuations   The behavior of a stationary inverted point mass pendulum pivoted at its
lower end in a gravitational potential is studied under the influence of
statistical fluctuations. It is shown using purely classical equations that the
pendulum eventually tips over i.e evolves out of its initial position of
unstable equilibrium, and, in a finite amount of time points down assuming a
position of stable equilibrium. This `tipping time' is calculated by solving
the appropriate Fokker- Planck equation in the overdamped limit. It is also
shown that the asymptotic time solution for probability corresponds to the
Boltzmann distribution, as expected for a system in stable equilibrium, and
that the tipping time tends to infinity as the parameter corresponding to the
strength of thermal fluctuations is tuned to zero, thereby defining the limit
where one recovers the classical result that a stationary inverted point mass
pendulum never tips over. The paper provides a unique perspective showing that
phenomena like tipping that have been often attributed to quantum mechanics can
be studied even in the domain of purely classical physics.

10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math