A version of a matrix method in statistical mechanics

V. I. Skripnik

Dietmar R. A. Johlen

Vyacheslav I. Yukalov

Ian D. Lawrie

The relationship between two approaches to the study of non-equilibrium field theories, namely quantum statistical mechanics and thermo field dynamics, is investigated. The formalism of superoperators acting in the Liouville space of density matrices is used to provide a detailed translation between the two approaches. It is found that thermo field dynamics is exactly equivalent to a restricted version of quantum statistical mechanics, in which the initial density matrix is constrained to be Gaussian. The dissipative perturbation theory developed within thermo field dynamics is translated into the language of statistical mechanics, and is found to be equivalent to that devised by the author using the statistical-mechanical closed-time-path method, except that the latter theory is not restricted to Gaussian initial states.

F. A. R. Navarro, J. F. V. Flores

Herein, in the context of third version of nonextensive statistical mechanics, theory that generalize the Boltzmann-Gibbs-Shannon statistics, we displayed a solution for an anomaly found by calculating the internal energy for a composite A+B, of 2 spines 1/2, with additive Hamiltonian H= HA+ HB; specifically, the calculation of the internal energy in the full Hilbert space is different from the calculation done in the Hilbert subspaces, in other words, Utot is different to UA +UB. We carry out analytical calculations (for 2 spins 1/2). The results exactly indicate that the alternative method of matrices EA and EB is suitable for the calculations of the internal energy, therefore, the matrix that contains the physical information of the system is the matrix rho^q and not rho, as happen in the standard statistical.

Osvaldo Civitarese, Manuel Gadella