Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variance of fluctuations from Noether invariance   The strength of fluctuations, as measured by their variance, is paramount in
the quantitative description of a large class of physical systems, ranging from
simple and complex liquids to active fluids and solids. Fluctuations originate
from the irregular motion of thermal degrees of freedom and statistical
mechanics facilitates their description. Here we demonstrate that fluctuations
are constrained by the inherent symmetries of the given system. For
particle-based classical many-body systems, Noether invariance at second order
in the symmetry parameter leads to exact sum rules. These identities
interrelate the global force variance with the mean potential curvature.
Noether invariance is restored by an exact balance between these distinct
mechanisms. The sum rules provide an important guide for assessing and
constructing theories, for ensuring self-consistency in simulation work, and
for providing a systematic pathway to the theoretical quantification of
fluctuations.

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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
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The categories of this paper are: astro-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom