Thermodynamic extension of density-functional theory. I. Basic Massieu function, its Legendre and Massieu-Planck transforms for equilibrium state in terms of density matrix - Physics > Chemical PhysicsReport as inadecuate




Thermodynamic extension of density-functional theory. I. Basic Massieu function, its Legendre and Massieu-Planck transforms for equilibrium state in terms of density matrix - Physics > Chemical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: A general formulation of the equilibrium state of a many-electron system interms of a mixed-state, ensemble density matrix operator in the Fock space,based on the maximum entropy principle, is introduced. Various characteristicfunctions-functionals are defined and investigated: the basic Massieu functionfor fully open thermodynamic system ensemble, the effective action functionfor the fully closed isolated system, and a series of Legendre transforms forpartially open-closed ones - the Massieu functions. Convexity and-or concavityproperties of these functions are determined, their first and secondderivatives with respect to all arguments are obtained. Other characteristicfunctions - the Gibbs-Helmholtz functions - are obtained from previous ones astheir Massieu-Planck transforms, i.e. by specific transformation of argumentswhich involves the temperature and by applying the temperature with the minusas a prefactor. Such functions are closer to traditional Gibbs, Helmholtzthermodynamic potentials. However, the first and second derivatives of thesefunctions represent more complicated expressions than derivatives of theMassieu functions. All introduced functions are suitable for application to theextensions of the density functional theory, both at finite and zerotemperature.



Author: Robert Balawender, Andrzej Holas

Source: https://arxiv.org/







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