Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sojourn probabilities in tubes and pathwise irreversibility for It\^o
  processes   The sojourn probability of an It\^o diffusion process, that is its
probability to remain in the tubular neighborhood of a smooth path, is a
central quantity in the study of path probabilities. Previous works considered
the sojourn probability in the limit of vanishing tube radius, and employed the
metric induced by the diffusion tensor, rather than that of the ambient space,
to define the tube enclosing the smooth path. This presents two difficulties in
experimentally measuring sojourn probabilities: first, the state-dependence of
the diffusion tensor is not known apriori, and second, the limit has to be
accessed through a sequence of measurements at finite tube radius. Here we
circumvent these difficulties by obtaining a general expression for the sojourn
probability of $N$-dimensional It\^o processes in tubes whose radii are small
but finite, and fixed by the metric of the ambient Euclidean space. The central
quantity in our study is the rate at which trajectories leave the tube for the
first time. This has an interpretation as a Lagrangian and can be measured
directly in experiment. We find that this Lagrangian differs, in general, from
the Onsager-Machlup Lagrangian and has a form not previously reported in the
literature. We confirm our result by comparing to numerical simulations for a
one-dimensional diffusion process with state-dependent diffusivity. We
demonstrate that the most probable tube for a barrier crossing depends
sensitively on the tube radius. We find that that while in the limit of
vanishing tube radius the ratio of sojourn probabilities for a pair of distinct
paths is in general divergent, the same for a path and its time-reversal is
always convergent and finite. This provides, in turn, a pathwise definition of
irreversibility for It\^o processes that is agnostic to the state-dependence of
the diffusion tensor.

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The categories of this paper are: nlin
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The categories of this paper are: math
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th