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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.

Classical analogue of the statistical operator

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Plastino A., Plastino A., Zander C.

Open Physics

2014

vol. 12

issue 3

168-174

We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system.

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2 Open Physics

1 2014

1 2012

2 Plastino A.

1 Flego S.

1 Zander C.

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Physical implications of Fisher-information’s scaling symmetry

Classical analogue of the statistical operator