Nonextensive thermodynamics of the two-site Hubbard model:Canonical ensembles

Józef Spałek, Andrzej M. Oleś, K. A. Chao

F. A. R. Navarro, E. Torres Tapia, Pedro Pacheco Peña

Abstract We hereby introduce a research about a grand canonical ensemble for the extended two-site Hubbard model, that is, we consider the intersite interaction term in addition to those of the simple Hubbard model. To calculate the thermodynamical parameters, we utilize the nonextensive statistical mechanics; specifically, we perform the simulations of magnetic internal energy, specific heat, susceptibility, and thermal mean value of the particle number operator. We found out that the addition of the intersite interaction term provokes a shifting in all the simulated curves. Furthermore, for some values of the on-site Coulombian potential, we realize that, near absolute zero, the consideration of a chemical potential varying with temperature causes a nonzero entropy. PACS 75.10.Jm, 05.30.-d, 65.80.+n

J. P. F. LeBlanc, Emanuel Gull

J. F. V. Flores

We study a system formed by M dimers through half-filled two-site Hubbard model, with two electrons. Our approach use the third version of Nonextensive Statistical Mechanics as tool for calculating thermodynamic and magnetic parameters such as entropy, internal energy, magnetization and specific heat. In the computer simulations, we vary the q entropic index values between 1 and 2, such that, q = 1.0, 1.4, 1.7 and 2.0. These values are interesting to study small magnetic systems. We find the critical temperature regions in simulations with the simple Hubbard model, i.e. without the intersite interaction. For other side, adding this additional term, we notice an enlargement and shifting of the thermodynamic parameters comparing with the obtained from simple Hubbard model; even more, we found in some cases the absence of the critical temperature regions.

D. Grensing, Heinz Koppe

Hui-yi Tang, Jian-Hui Wang, Yongli Ma

For a small system at a low temperature, thermal fluctuation and quantum effect play important roles in quantum thermodynamics. Starting from micro-canonical ensemble, we generalize the Boltzmann–Gibbs statistical factor from infinite to finite systems, no matter the interactions between particles are considered or not. This generalized factor, similar to Tsallis’s q-form as a power-law distribution, has the restriction of finite energy spectrum and includes the nonextensivities of the small systems. We derive the exact expression for distribution of average particle numbers in the interacting classical and quantum nonextensive systems within a generalized canonical ensemble. This expression in the almost independent or elementary excitation quantum finite systems is similar to the corresponding ones obtained from the conventional grand-canonical ensemble. In the reconstruction for the statistical theory of the small systems, we present the entropy of the equilibrium systems and equation of total thermal energy. When we investigate the thermodynamics for the interacting nonextensive systems, we obtain the system–bath heat exchange and “uncompensated heat” which are in the thermodynamical level and independent on the detail of the system–bath coupling. For ideal finite systems, with different traps and boundary conditions, we calculate some thermodynamic quantities, such as the specific heat, entropy, and equation of state, etc. Particularly at low temperatures for the small systems, we predict some novel behaviors in the quantum thermodynamics, including internal entropy production, heat exchanges between the system and its surroundings and finite-size effects on the free energy.