Related papers: Generalized Wigner-von Neumann entropy and its typ…
Eugene Wigner's revolutionary vision predicted that the energy levels of large complex quantum systems exhibit a universal behavior: the statistics of energy gaps depend only on the basic symmetry type of the model. Simplified models of…
We used the von Neumann entropy to study the single and many-particle on-site localizations of stationary states for an anisotropic Heisenberg spin-1/2 chain. With a constructed bounded sequence of on-site energies for single and…
We present a partition of quantum observables in an open quantum system which is inherited from the division of the underlying Hilbert space or configuration space. It is shown that this partition leads to the definition of an inhomogeneous…
We propose a formal extension of thermodynamics and kinetic theories to a larger class of entropy functionals. Kinetic equations associated to Boltzmann, Fermi, Bose and Tsallis entropies are recovered as a special case. This formalism…
Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase…
A large class of strongly correlated quantum systems can be described in certain large-N limits by quadratic in field actions along with self-consistency equations that determine the two-point functions. We use the replica approach and the…
By considering matter as a constraint on the availability of gravitational degrees of freedom and accounting for the statistical interpretation of Rindler horizons, the freedom to construct quantum gravity theories reproducing General…
The Koopman--von Neumann (KvN) formulation of spectrally truncated fluid and plasma dynamics is considered as a potential approach for quantum computation. The KvN framework embeds the Liouville equation into a Hilbert space with…
We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral…
Von Neumann entropy (VNE) is a fundamental quantity in quantum information theory and has recently been adopted in machine learning as a spectral measure of diversity for kernel matrices and kernel covariance operators. While maximizing VNE…
In the type II von Neumann algebras that appear in semiclassical gravity, all states have infinite entropy, but entropy differences are uniquely defined. Akers and I have shown that the entropy difference of microcanonical states has a…
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L,…
We propose a generalization of the Wasserstein distance of order 1 to the quantum states of $n$ qudits. The proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance…
Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs'…
The Hamiltonian approach to the General Relativity and the Standard Model is studied in the context of its consistency with the Newton law, the Higgs effect, the Hubble cosmological evolution and the Cosmic Microwave Background radiation…
We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
Wigner's celebrated theorem, which is particularly important in the mathematical foundations of quantum mechanics, states that every bijective transformation on the set of all rank-one projections of a complex Hilbert space which preserves…
A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…
We prove that any asymptotics of a finite-dimensional quantum Markov processes can be formulated in the form of a generalized Jaynes principle in the discrete as well as in the continuous case. Surprisingly, we find that the open system…