Unnormalized nonextensive expectation value and zeroth law of thermodynamics

We show an attempt to establish the zeroth law of thermodynamics within the framework of nonextensive statistical mechanics based on the classic normalization $\texttt{Tr}\hat{\rho}=1$ and the unnormalized expectation $x=\texttt{Tr}\hat{\rho}^q\hat{x}$. The first law of thermodynamics and the definition of heat and work in this formalism are discussed.Comment: 6 pages, no figure, RevTeX. To appear in Chaos, Solitons & Fractals (2002

Extensive generalization of statistical mechanics based on incomplete information theory

Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization $\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln p_i$. The concomitant incomplete statistical mechanics is applied to some physical systems in order to show the effect of the incompleteness of information. It is shown that this extensive generalized statistics can be useful for the correlated electron systems in weak coupling regime.Comment: 15 pages, 3 eps figures, Te

Correlated electrons and generalized statistics

Several important generalizations of Fermi-Dirac distribution are compared to numerical and experimental results for correlated electron systems. It is found that the quantum distributions based on incomplete information hypothesis can be useful for describing this kind of systems. We show that the additive incomplete fermion distribution gives very good description of weakly correlated electrons and that the nonadditive one is suitable to very strong correlated cases.Comment: 13 pages, RevTex file, 4 ps figures. The European Physical Journal B (2002), in pres

First-principles investigation of dynamical properties of molecular devices under a steplike pulse

We report a computationally tractable approach to first principles investigation of time-dependent current of molecular devices under a step-like pulse. For molecular devices, all the resonant states below Fermi level contribute to the time-dependent current. Hence calculation beyond wideband limit must be carried out for a quantitative analysis of transient dynamics of molecules devices. Based on the exact non-equilibrium Green's function (NEGF) formalism of calculating the transient current in Ref.\onlinecite{Maciejko}, we develop two approximate schemes going beyond the wideband limit, they are all suitable for first principles calculation using the NEGF combined with density functional theory. Benchmark test has been done by comparing with the exact solution of a single level quantum dot system. Good agreement has been reached for two approximate schemes. As an application, we calculate the transient current using the first approximated formula with opposite voltage $V_L(t)=-V_R(t)$ in two molecular structures: Al-${\rm C}_{5}$-Al and Al-${\rm C}_{60}$-Al. As illustrated in these examples, our formalism can be easily implemented for real molecular devices. Importantly, our new formula has captured the essential physics of dynamical properties of molecular devices and gives the correct steady state current at $t=0$ and $t\rightarrow \infty$.Comment: 15 pages, 8 figure