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Physical implications of Fisher-information’s scaling symmetry

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Flego S., Plastino A., Plastino A.

Open Physics

2012

vol. 10

issue 2

390-397

We study the scaling properties of Fisher’s information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher’s measure I and encounter that, from the concomitant operating rules, several interesting, albeit known, results can be derived. This entails that such results can be regarded as pre-configured by the conjunction of scaling and information theory. The central notion to be arrived at is that scaling entails that I must obey a certain partial differential equation (PDE). These PDE-solutions have properties that enable the application of a Legendre-transform (LT). The conjunction PDE+LT leads one to obtain several quantum results without recourse to the Schrödinger’s equation.

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1 Open Physics

1 2012

1 Flego S.

1 Plastino A.

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Physical implications of Fisher-information’s scaling symmetry