### Abstract

Ghosh, Berkowitz and Parr designed a thermodynamical transcription of the ground-state density functional theory and introduced a local temperature that varies from point to point. The theory, however, is not unique because the kinetic energy density is not uniquely defined. Here we derive the expression of the phase-space Fisher information in the GBP theory taking the inverse temperature as the Fisher parameter. It is proved that this Fisher information takes its minimum for the case of constant temperature. This result is consistent with the recently proven theorem that the phase-space Shannon information entropy attains its maximum at constant temperature.

Original language | English |
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Pages (from-to) | 149-152 |

Number of pages | 4 |

Journal | Chemical Physics Letters |

Volume | 695 |

DOIs | |

Publication status | Published - Mar 1 2018 |

### Fingerprint

### Keywords

- Density functional theory
- Fisher information

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

**Thermodynamical transcription of density functional theory with minimum Fisher information.** / Nagy, A.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Thermodynamical transcription of density functional theory with minimum Fisher information

AU - Nagy, A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - Ghosh, Berkowitz and Parr designed a thermodynamical transcription of the ground-state density functional theory and introduced a local temperature that varies from point to point. The theory, however, is not unique because the kinetic energy density is not uniquely defined. Here we derive the expression of the phase-space Fisher information in the GBP theory taking the inverse temperature as the Fisher parameter. It is proved that this Fisher information takes its minimum for the case of constant temperature. This result is consistent with the recently proven theorem that the phase-space Shannon information entropy attains its maximum at constant temperature.

AB - Ghosh, Berkowitz and Parr designed a thermodynamical transcription of the ground-state density functional theory and introduced a local temperature that varies from point to point. The theory, however, is not unique because the kinetic energy density is not uniquely defined. Here we derive the expression of the phase-space Fisher information in the GBP theory taking the inverse temperature as the Fisher parameter. It is proved that this Fisher information takes its minimum for the case of constant temperature. This result is consistent with the recently proven theorem that the phase-space Shannon information entropy attains its maximum at constant temperature.

KW - Density functional theory

KW - Fisher information

UR - http://www.scopus.com/inward/record.url?scp=85041804571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041804571&partnerID=8YFLogxK

U2 - 10.1016/j.cplett.2018.02.009

DO - 10.1016/j.cplett.2018.02.009

M3 - Article

AN - SCOPUS:85041804571

VL - 695

SP - 149

EP - 152

JO - Chemical Physics Letters

JF - Chemical Physics Letters

SN - 0009-2614

ER -