No abstract

By introducing a functional of the reduced density matrix, we generalize the definition of a quantum entropy which incorporates the indistinguishability principle of a system of identical particles. With the present definition, the principle of quantum maximum entropy permits us to solve the closure problem for a quantum hydrodynamic set of balance equations corresponding to an arbitrary number of moments in the framework of extended thermodynamics. The determination of the reduced Wigner function for equilibrium and nonequilibrium conditions is found to become possible only by assuming that the Lagrange multipliers can be expanded in powers of variant Planck's over 2pi(2). Quantum contributions are expressed in powers of variant Planck's over 2pi(2) while classical results are recovered in the limit variant Planck's over 2pi-->0 .

We use a density matrix formalism to derive a kinetic theory for a quantum gas. Generalized kinetic fields are introduced and, employing the Wigner function, a certain hierarchy of quantum hydrodynamic (QHD) equations for the corresponding macroscopic variables is obtained. We assert a maximum entropy principle to obtain closure of the QHD system. For the explicit incorporation of statistics a proper quantum entropy is analyzed in terms of the reduced density matrix. The determination of the reduced Wigner function for equilibrium and non-equilibrium conditions is found to become possible only by assuming that the Lagrange multipliers can be expanded in powers of ℏ2. Quantum contributions are expressed in powers of ℏ2 while classical results are recovered in the limit ℏ → 0.

We derive, using the entropy maximum principle, an expression for the distribution function of carriers as a function of a set of macroscopic quantities ͑density, velocity, energy, deviatoric stress, heat flux͒. Given the distribution function, we can obtain a hydrodynamic model in which all the constitutive functions ͑fluxes and collisional productions͒ are explicitly computed starting from their kinetic expressions. We have applied our model to the simulation of the thermodynamic properties of bulk silicon and of some n ϩ nn ϩ submicrometer Si devices ͑with several doping profiles and applied biases͒, obtaining results comparable with Monte Carlo simulations. Computation times are of order of few seconds for a picosecond of simulation. ͓S0163-1829͑98͒01607-5͔

Using the Wigner representation, compatibly with the uncertainty principle, we formulate a quantum maximum entropy principle for the fractional exclusion statistics. By considering anyonic systems satisfying fractional exclusion statistic, all the results available in the literature are generalized in terms of both the kind of statistics and a nonlocal description for excluson gases. Gradient quantum corrections are explicitly given at different levels of degeneracy and classical results are recovered when ℏ→0.