Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic action for tubes: Connecting path probabilities to
  measurement   The trajectories of diffusion processes are continuous but
non-differentiable, and each occurs with vanishing probability. This introduces
a gap between theory, where path probabilities are used in many contexts, and
experiment, where only events with non-zero probability are measurable. Here we
bridge this gap by considering the probability of diffusive trajectories to
remain within a tube of small but finite radius around a smooth path. This
probability can be measured in experiment, via the rate at which trajectories
exit the tube for the first time, thereby establishing a link between path
probabilities and physical observables. Considering $N$-dimensional overdamped
Langevin dynamics, we show that the tube probability can be obtained
theoretically from the solution of the Fokker-Planck equation. Expressing the
resulting exit rate as a functional of the path and ordering it as a power
series in the tube radius, we identify the zeroth-order term as the
Onsager-Machlup stochastic action, thereby elevating it from a mathematical
construct to a physical observable. The higher-order terms reveal, for the
first time, the form of the finite-radius contributions which account for
fluctuations around the path. To demonstrate the experimental relevance of this
action functional for tubes, we numerically sample trajectories of Brownian
motion in a double-well potential, compute their exit rate, and show an
excellent agreement with our analytical results. Our work shows that smooth
tubes are surrogates for non-differentiable diffusive trajectories, and provide
a direct way of comparing theoretical results on single trajectories, such as
path-wise definitions of irreversibility, to measurement.

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat