Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hellmann-Feynman connection for the relative Fisher information   The $(i)$ reciprocity relations for the relative Fisher information (RFI,
hereafter) and $(ii)$ a generalized RFI-Euler theorem, are self-consistently
derived from the Hellmann-Feynman theorem. These new reciprocity relations
generalize the RFI-Euler theorem and constitute the basis for building up a
mathematical Legendre transform structure (LTS, hereafter), akin to that of
thermodynamics, that underlies the RFI scenario. This demonstrates the
possibility of translating the entire mathematical structure of thermodynamics
into a RFI-based theoretical framework. Virial theorems play a prominent role
in this endeavor, as a Schr\"odinger-like equation can be associated to the
RFI. Lagrange multipliers are determined invoking the RFI-LTS link and the
quantum mechanical virial theorem. An appropriate ansatz allows for the
inference of probability density functions (pdf's, hereafter) and
energy-eigenvalues of the above mentioned Schr\"odinger-like equation. The
energy-eigenvalues obtained here via inference are benchmarked against
established theoretical and numerical results. A principled theoretical basis
to reconstruct the RFI-framework from the FIM framework is established.
Numerical examples for exemplary cases are provided.

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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph