Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical physics of long dynamical trajectories for a system in
  contact with several thermal reservoirs   For a system in contact with several reservoirs $r$ at different
inverse-temperatures $\beta_r$, we describe how the Markov jump dynamics with
the generalized detailed balance condition can be analyzed via a statistical
physics approach of dynamical trajectories $[{\cal C}(t)]_{0 \leq t \leq T} $
over a long time interval $T \to + \infty$. The relevant intensive variables
are the time-empirical density $\rho(\cal C)$, that measures the fractions of
time spent in the various configurations ${\cal C}$, and the time-empirical
jump densities $k_r ({\cal C', \cal C}) $, that measure the frequencies of
jumps from configuration ${\cal C} $ to configuration ${\cal C '} $ when it is
the reservoir $r$ that furnishes or absorbs the corresponding energy difference
($E({\cal C '})- E({\cal C })$).

26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin