Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transient probability currents provide upper and lower bounds on
  non-equilibrium steady-state currents in the Smoluchowski picture   Probability currents are fundamental in characterizing the kinetics of
non-equilibrium processes. Notably, the steady-state current $J_{ss}$ for a
source-sink system can provide the exact mean-first-passage time (MFPT) for the
transition from source to sink. Because transient non-equilibrium behavior is
quantified in some modern path sampling approaches, such as the "weighted
ensemble" strategy, there is strong motivation to determine bounds on $J_{ss}$
-- and hence on the MFPT -- as the system evolves in time. Here we show that
$J_{ss}$ is bounded from above and below by the maximum and minimum,
respectively, of the current as a function of the spatial coordinate at any
time $t$ for one-dimensional systems undergoing over-damped Langevin (i.e.,
Smoluchowski) dynamics and for higher-dimensional Smoluchowski systems
satisfying certain assumptions when projected onto a single dimension. These
bounds become tighter with time, making them of potential practical utility in
a scheme for estimating $J_{ss}$ and the long-timescale kinetics of complex
systems. Conceptually, the bounds result from the fact that extrema of the
transient currents relax toward the steady-state current.

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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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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: q-fin
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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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: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys