We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.
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21 July 2013
Research Article|
July 18 2013
Functional thermo-dynamics: A generalization of dynamic density functional theory to non-isothermal situations
Jesús G. Anero;
Jesús G. Anero
1Dept. Física Fundamental,
Universidad Nacional de Educación a Distancia
, Aptdo. 60141, E-28080 Madrid, Spain
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Pep Español;
Pep Español
1Dept. Física Fundamental,
Universidad Nacional de Educación a Distancia
, Aptdo. 60141, E-28080 Madrid, Spain
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Pedro Tarazona
Pedro Tarazona
2Dept. Física Teórica de la Materia Condensada, Condensed Matter Physics Center IFIMAC,
Universidad Autónoma de Madrid
, E-28049 Madrid, Spain
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J. Chem. Phys. 139, 034106 (2013)
Article history
Received:
February 18 2013
Accepted:
June 05 2013
Citation
Jesús G. Anero, Pep Español, Pedro Tarazona; Functional thermo-dynamics: A generalization of dynamic density functional theory to non-isothermal situations. J. Chem. Phys. 21 July 2013; 139 (3): 034106. https://doi.org/10.1063/1.4811655
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