### Abstract

Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini-Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.

Original language | English |
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Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

DOIs | |

Publication status | Accepted/In press - Apr 5 2016 |

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### Keywords

- Canonical distribution function
- Density functional theory
- Fisher information

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Phase space view of quantum mechanical systems and Fisher information.** / Nagy, A.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Phase space view of quantum mechanical systems and Fisher information

AU - Nagy, A.

PY - 2016/4/5

Y1 - 2016/4/5

N2 - Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini-Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.

AB - Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini-Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.

KW - Canonical distribution function

KW - Density functional theory

KW - Fisher information

UR - http://www.scopus.com/inward/record.url?scp=84965174555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84965174555&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2016.05.006

DO - 10.1016/j.physleta.2016.05.006

M3 - Article

AN - SCOPUS:84965174555

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

ER -