Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variational characterization of Langevin$\boldsymbol{-}$Smoluchowski
  diffusions   We show that Langevin$-$Smoluchowski measure on path space is invariant under
time-reversal, followed by stochastic control of the drift with a novel
entropic-type criterion. Repeated application of these forward-backward steps
leads to a sequence of stochastic control problems, whose initial/terminal
distributions converge to the Gibbs probability measure of the diffusion, and
whose values decrease to zero along the relative entropy of the
Langevin$-$Smoluchowski flow with respect to this Gibbs measure.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an