Entropy is a concept which appears in several fields and it is in the center of interest both in
mathematical and physical subjects, sometimes even at other places, for example in …

It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting
can be considered as a Gibbs state associated with Hamiltonian with commuting nearest …

In the present paper, we propose a refinement for the notion of quantum Markov states
(QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any …

The main aim of the present paper is to prove the existence of a phase transition in quantum
Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind …

In this paper, we continue the investigation of quantum Markov states (QMS) and define their
mean entropies. Such entropies are explicitly computed under certain conditions. The …

We introduce the notion of Markov states and chains on the Canonical Anticommutation
Relations algebra over ℤ, emphasizing some remarkable differences with the infinite tensor …

We introduce quantum Markov states (QMS) in a general tree graph G=(V, E) G=(V, E),
extending the Cayley tree's case. We investigate the Markov property wrt the finer structure …

In this paper we consider nearest-neighbours models, where the spin takes values in the set
Φ={η1, η1,…, ηq} and is assigned to the vertices of the Cayley tree Γk. The Hamiltonian is …

We clarify the meaning of diagonalizability of quantum Markov states. Then, we prove that
each non homogeneous quantum Markov state is diagonalizable. Namely, for each Markov …

We construct an uncountable family of pairwise non-conjugate non-Bernoullian K-systems of
type III 1 with the same finite CNT-entropy. We also investigate clustering properties of …