Time-dependent density functional theory as a thermodynamics

Int J of Quantum Chemistry

2021

Relationship of Fisher information and density functional theory is reviewed. Links between the Fisher and Shannon information, the local wave‐vector and the relative information are displayed. Euler equations for the Fisher and relative Fisher information are presented. A combined information theoretical and thermodynamic view of density functional theory is analyzed. The extremum of the Shannon and Fisher information results a constant temperature and for Coulomb systems a simple relation between the total energy and phase‐space Fisher information. Relations for phase‐spase fidelity, fidelity susceptibility and relative information are also presented.

Section: Introductionmentioning

confidence: 99%

Fisher information and density functional theory

Int J of Quantum Chemistry

2021

“…It was possible to define local entropy, free energy, and to establish an analogy with the classical thermodynamics of fluids . There have been several extension of the formalism . There are some new developments in applying and understanding the Ghosh–Berkowitz–Parr entropy …”

Section: Introductionmentioning

confidence: 99%

“…[2] There have been several extension of the formalism. [6][7][8][9][10][11][12][13][14][15][16] There are some new developments in applying and understanding the Ghosh-Berkowitz-Parr entropy. [17][18][19][20][21][22][23] The local temperature of Ghosh et al was defined via the kinetic energy density and varies from point to point.…”

mentioning

confidence: 99%

Thermodynamical transcription of the density functional theory with constant temperature

Int J of Quantum Chemistry

2017

The thermodynamical interpretation of the density functional theory for an electronic ground state is revisited. Ghosh et al. invented the thermodynamical transcription of the ground-state density functional theory into a local thermodynamics. They introduced the idea of the local temperature that varies from point to point. The local temperature is defined via the kinetic energy density. The kinetic energy density is not uniquely defined, usually the everywhere positive gradient form is applied. Now we prove that it is possible selecting the kinetic energy density so that the local temperature be a constant for the whole system under consideration. The kinetic energy density is proportional to the electron density and the temperature is proportional to the kinetic energy. Furthermore, the kinetic energy density corresponding to the constant temperature, maximizes the information entropy.density functional theory, information entropy, thermodynamical transcription | I N T R O D U C T I O NMore than three decades ago Ghosh et al. wrote a paper [1] entitled "Transcription of ground-state density functional theory into a local thermodynamics." They obtained a phase-space distribution function fðr; pÞ by maximizing a phase-space Shannon information entropy subject to the conditions that f yields the density nðrÞ and the local kinetic energy density of the system. A local Maxwell-Boltzmann distribution function was resulted.They introduced the concept of local temperature. This formalism has been used in several applications. [2,3] For example, approximate expressions for the exchange energy were derived. [4,5] It was possible to define local entropy, free energy, and to establish an analogy with the classical thermodynamics of fluids. [2] There have been several extension of the formalism. [6][7][8][9][10][11][12][13][14][15][16] There are some new developments in applying and understanding the Ghosh-Berkowitz-Parr entropy. [17][18][19][20][21][22][23] The local temperature of Ghosh et al. was defined via the kinetic energy density and varies from point to point. However, the kinetic energy density is not uniquely defined. Adding a term that integrates to zero to the kinetic energy density results another kinetic energy density with the same kinetic energy but different local temperature. Usually, the gradient form of the kinetic energy density is applied, because it is everywhere positive. Now we prove that it is possible selecting the kinetic energy density so that the local temperature be a constant for the whole system under consideration. The kinetic energy density is proportional to the electron density and the temperature is proportional to the kinetic energy. Moreover, the kinetic energy density corresponding to the constant temperature, maximizes the information entropy. This very simple interpretation gives a new insight into the density functional theory. Analytical examples for the linear harmonic oscillator and the H-atom are presented.In the following section, the Ghosh-Berkowitz-Parr theory is ...

“…Local entropy, free energy were defined and the analogy with the classical thermodynamics of fluids was founded [6]. The formalism has been generalized in several ways [7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Phase space view of quantum mechanical systems and Fisher information

2016

Physics Letters A

Self Cite

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.