Legendre-transform structure derived from quantum theorems
S. P. Flego, A. Plastino, and A. R. Plastino
TL;DR
This paper reveals a Legendre-transform structure in quantum mechanics derived from the Hellmann-Feynman and Virial theorems, highlighting deep links between Fisher information, Schrödinger's equation, and thermodynamics.
Contribution
It introduces a novel information-theoretic framework connecting quantum equations with thermodynamic structures using Fisher's information measure.
Findings
Legendre-transform structure in Schrödinger's equation uncovered
Fisher information links quantum mechanics and thermodynamics
New evidence for information-theoretic connections in physics
Abstract
By recourse to i) the Hellmann-Feynman theorem and ii) the Virial one, the information-optimizing principle based on Fisher's information measure uncovers a Legendre-transform structure associated with Schr\"odinger's equation, in close analogy with the structure that lies behind the standard thermodynamical formalism. The present developments provide new evidence for the information theoretical links based on Fisher's measure that exist between Schr\"odinger's equation, on the one hand, and thermodynamics/thermostatistics on the other one.
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