Related papers: A Construction of Dynamical Entropy on CAR Algebra…
In this paper a formalism for studying the dynamics of quantum systems coupled to classical spin environments is reviewed. The theory is based on generalized antisymmetric brackets and naturally predicts open-path off-diagonal geometric…
We study the entropy of pure shift-invariant states on a quantum spin chain. Unlike the classical case, the local restrictions to intervals of length $N$ are typically mixed and have therefore a non-zero entropy $S_N$ which is, moreover,…
Von Neumann entropy production rates of the quantised kicked rotor interacting with an environment are calculated. A significant correspondence is found between the entropy contours of the classical and quantised systems. This is a…
A major topic of (classical) ergodic theory is to examine qualitatively how the phase space of dynamical systems is penetrated by the orbits of their dynamics. We consider interacting qubit systems with dynamics according to 4-local…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
We propose a new formula for the entropy of a dynamical black hole$-$valid to leading order for perturbations off of a stationary black hole background$-$in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in $n$…
Measuring the average information that is necessary to describe the behaviour of a dynamical system leads to a generalization of the Kolmogorov-Sinai entropy. This is particularly interesting when the system has null entropy and the…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
Quantum Information is a new area of research which has been growing rapidly since last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more…
In this article we provide, from a novel perspective, arguments that support the idea that, in the wake of Cox' approach to probability theory, von Neumann's entropy should be the natural one in Quantum Mechanics. We also generalize the…
The fermionic von Neumann entropy, the fermionic entanglement entropy and the fermionic relative entropy are defined for causal fermion systems. Our definition makes use of entropy formulas for quasi-free fermionic states in terms of the…
We compute the von Neumann and generalized R\'{e}nyi entanglement entropies in the ground-state of the spin-1/2 antiferromagnetic Heisenberg model on the square lattice using the modified spin-wave theory for finite lattices. The addition…
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in…
We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the…
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate…
In quantum information theory, von Neumann entropy plays an important role. The entropies can be obtained analytically only for a few states. In continuous variable system, even evaluating entropy numerically is not an easy task since the…
It is von Neumann who opened the window for today's Information epoch. He defined quantum entropy including Shannon's information more than 20 years ahead of Shannon, and he introduced a concept what computation means mathematically. In…
Recently, an {\it algebraic-dynamical theory} (ADT) for strongly interacting many-body quantum Hamiltonians in W. Ding, arXiv: 2202.12082 (2022). By introducing the complete operator basis set, ADT proposes a generic framework for…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…