Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5102369 | Physica A: Statistical Mechanics and its Applications | 2018 | 10 Pages |
Abstract
The Tsallis relative entropy Sq(ÏË,ÏË) measures the distance between two arbitrary density matrices ÏË and ÏË. In this work the approximation to this quantity when q=1+δ (δâª1) is obtained. It is shown that the resulting series is equal to the von Neumann relative entropy when δ=0. Analyzing the von Neumann relative entropy for an arbitrary ÏË and a thermal equilibrium state ÏË=eâβHËâTr(eâβHË) is possible to define a new inequality relating the energy, the entropy, and the partition function of the system. From this inequality, a parameter that measures the distance between the two states is defined. This distance is calculated for a general qubit system and for an arbitrary unimodal Gaussian state. In the qubit case, the dependence on the purity of the system is studied for Tâ¥0 and also for T<0. In the Gaussian case the general partition function, given a unimodal quadratic Hamiltonian, is calculated and the comparison of the thermal light state as a thermal equilibrium state of the parametric amplifier is presented.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
J.A. López-SaldÃvar, O. Castaños, M.A. Man'ko, V.I. Man'ko,