相关论文: Note on exponential families of distributions
The exponential family of models is defined in a general setting, not relying on probability theory. Some results of information geometry are shown to remain valid. Exponential families both of classical and of quantum mechanical…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…
It is shown that a small system in thermodynamic equilibrium with a finite thermostat can have a q-exponential probability distribution which closely depends on the energy nonextensivity and the particle number of the thermostat. The…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles…
The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown…
We discuss the possibility of using generalized canonical distributions, i.e. using other factors than $\exp(-\beta E)$, in order to compute the equilibrium properties of physical systems. It will be show that some other choices can, in…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean {\mu}…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation.
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
We discover numerically that a moving wave packet in a quantum chaotic billiard will always evolve into a quantum state, whose density probability distribution is exponential. This exponential distribution is found to be universal for…
The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical…
Description of system containing classical and quantum subsystems by means of tomographic probability distributions is considered. Evolution equation of the system states is studied.
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…