Related papers: Generalized entropies in quantum and classical sta…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers.…
Motivated by the group entropy theory, in this work we generalize the algebra of real numbers (that we called G-algebra), from which we develop an associated G-differential calculus. Thus, the algebraic structures corresponding to the…
We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…
In this note we lay some groundwork for the resource theory of thermodynamics in general probabilistic theories (GPTs). We consider theories satisfying a purely convex abstraction of the spectral decomposition of density matrices: that…
Quantum field theory allows more general symmetries than groups and Lie algebras. For instance quantum groups, that is Hopf algebras, have been familiar to theoretical physicists for a while now. Nowdays many examples of symmetries of…
A number of the Fourier Series which occur in the theory of the semi-classical atom due to Englert and Schwinger are generalized and presented.
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum…
In this work, we show that it is possible to define a classical system associated with a Generalized Uncertainty Principle (GUP) theory via the implementation of a consistent symplectic structure. This provides a solid framework for the…
Recently, the R\'{e}nyi and Tsallis generalized entropies have extensively been used in order to study various cosmological and gravitational setups. Here, using a special type of generalized entropy, a generalization of both the R\'{e}nyi…
Suppose that $\alpha,\beta\in\mathbb{R}$. Let $\alpha\geqslant1$ and $c$ be a real number in the range $1<c< 12/11$. In this paper, it is proved that there exist infinitely many primes in the generalized Piatetski--Shapiro sequence, which…
Some problems related to an algebraic approach to quantum statistics are discussed. Generalized quantum statistics is described as a result of interactions. The Fock space representation is discussed. The problem of existence of…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. This approach has the advantage that statistical mechanics is much better…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
A new approach to the quantization of constrained or otherwise reduced classical mechanical systems is proposed. On the classical side, the generalized symplectic reduction procedure of Mikami and Weinstein, as further extended by Xu in…
Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…
We explore a possible application of the additive generalization of the Boltzmann-Gibbs-Shannon entropy proposed in [A.N. Gorban, I.V. Karlin, Phys. Rev. E, 67:016104 (2003)] to fully developed turbulence. The predicted probability…
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…