Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physically consistent numerical solver for time-dependent Fokker-Planck
  equations   We present a simple thermodynamically consistent method for solving
time-dependent Fokker--Planck equations (FPE) for over-damped stochastic
processes, also known as Smoluchowski equations. It yields both transition and
steady-state behavior and allows for computations of moment-generating and
large-deviation functions of observables defined along stochastic trajectories,
such as the fluctuating particle current, heat and work. The key strategy is to
approximate the FPE by a Master equation with transition rates in configuration
space that obey a local detailed balance condition for arbitrary
discretization. Its time-dependent solution is obtained by a direct computation
of the time-ordered exponential, representing the propagator of the FPE, by
summing over all possible paths in the discretized space. The method thus not
only preserves positivity and normalization of the solutions, but also yields a
physically reasonable total entropy production, regardless of the
discretization. To demonstrate the validity of the method and to exemplify its
potential for applications, we compare it against Brownian-dynamics simulations
of a heat engine based on an active Brownian particle trapped in a
time-dependent quartic potential.

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The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
19
The categories of this paper are: eess
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The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an