Generalized Entropies Depending Only on the Probability and Their Quantum Statistics

The generalized quantum statistics

We argue that the concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. With this, we make a conjecture that particles obey some generalized statistics that contains the quantum and classical statistics as special cases, where the level of overlappi...

Generalized Entanglement Entropies of Quantum Designs

Generalized relative entropies and the capacity of classical-quantum channels

We provide lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel. The lower bound is expressed in terms of the Hoe ding capacity, that we de ne similarly to the Holevo capacity, but replacing the relative entropy with the Hoe ding distance. Similarly, our upper bound is in terms of a quantity obtained by replacing the relative entropy w...

Entropies for complex systems: generalized-generalized entropies

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to – justified or not – hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann) we demonstrate how the corresponding entropy has to look like, given the form of the corresponding distribution functions. By two natural assumptions that (i) t...

On Multivariate Likelihood Ratio Ordering among Generalized Order Statistics and their Spacings

The most of the results obtained about stochastic properties of generalized order statistics and their spacings in the literature are based on equal model parameters. In this paper, with less restrictive conditions on the model parameters, we prove some new multivariate likelihood ratio ordering results between two sub-vectors of GOS's as well as two sub-vectors of $p$-spacings based on two con...