Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamic entropy as a Noether invariant   We study a classical many-particle system with an external control
represented by a time-dependent extensive parameter in a Lagrangian. We show
that thermodynamic entropy of the system is uniquely characterized as the
Noether invariant associated with a symmetry for an infinitesimal non-uniform
time translation $t\to t+\eta\hbar \beta$, where $\eta$ is a small parameter,
$\hbar$ is the Planck constant, $\beta$ is the inverse temperature that depends
on the energy and control parameter, and trajectories in the phase space are
restricted to those consistent with quasi-static processes in thermodynamics.

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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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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: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: eess