Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for
  the KPZ-Equation   We investigate the thermodynamic uncertainty relation for the $(1+1)$
dimensional Kardar-Parisi-Zhang equation on a finite spatial interval. In
particular, we extend the results for small coupling strengths obtained
previously to large values of the coupling parameter. It will be shown that,
due to the scaling behavior of the KPZ equation, the TUR product displays two
distinct regimes which are separated by a critical value of an effective
coupling parameter. The asymptotic behavior below and above the critical
threshold is explored analytically. For small coupling, we determine this
product perturbatively including the fourth order; for strong coupling we
employ a dynamical renormalization group approach. Whereas the TUR product
approaches a value of $5$ in the weak coupling limit, it asymptotically
displays a linear increase with the coupling parameter for strong couplings.
The analytical results are then compared to direct numerical simulations of the
KPZ equation showing convincing agreement.

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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio