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Phys Rev E. 2018 Feb;97(2-1):022128. doi: 10.1103/PhysRevE.97.022128.

Entropic bounds between two thermal equilibrium states.

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Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de Mexico, Apdo. Postal 70-543, 04510, CDMX, Mexico.
Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow Region 141700, Russia.
Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow 119991, Russia.
Department of Physics, Tomsk State University, Lenin Avenue 36, Tomsk 634050, Russia.


The positivity conditions of the relative entropy between two thermal equilibrium states ρ[over ̂]_{1} and ρ[over ̂]_{2} are used to obtain upper and lower bounds for the subtraction of their entropies, the Helmholtz potential and the Gibbs potential of the two systems. These limits are expressed in terms of the mean values of the Hamiltonians, number operator, and temperature of the different systems. In particular, we discuss these limits for molecules that can be represented in terms of the Franck-Condon coefficients. We emphasize the case where the Hamiltonians belong to the same system at two different times t and t^{'}. Finally, these bounds are obtained for a general qubit system and for the harmonic oscillator with a time-dependent frequency at two different times.


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