Search results for "Joint quantum entropy"
showing 10 items of 14 documents
Entanglement entropy in a periodically driven quantum Ising chain
2016
We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field, h(t), of a one-dimensional quantum Ising chain. We consider several realizations of h(t), and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After short-time relaxation, the dynamics of entanglement entropy synchronises with h(t), displaying an oscillatory behaviour at the frequency of the driving. Synchronisation in the dynamics of entanglement entropy, is spoiled by the appearance of quasi-revivals which fade out in the thermodynamic limit, and which we interpret using a quasi-particle picture ada…
Explicit Upper Bound for Entropy Numbers
2004
We give an explicit upper bound for the entropy numbers of the embedding I : W r,p(Ql) → C(Ql) where Ql = (−l, l)m ⊂ Rm, r ∈ N, p ∈ (1,∞) and rp > m.
Entropy, transverse entropy and partitions of unity
1994
AbstractThe topological entropy of a transformation is expressed in terms of partitions of unity. The transverse entropy of a flow tangential to a foliation is defined and expresed in a similar way. The geometric entropy of a foliation of a Riemannian manifold is compared with the transverse entropy of its geodesic flow.
An algorithmic construction of entropies in higher-order nonlinear PDEs
2006
A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film equation and the quantum drift–diffusion model. In all cases, an infinite number of entropy functionals together with the associated entropy productions is derived. Our technique can be extended to higher-order entropies, containing derivatives of the solution, and to several space dimensions. Furthermore, logarithmic Sobolev inequalities can …
Combinatorics of theSU(2)black hole entropy in loop quantum gravity
2009
We use the combinatorial and number-theoretical methods developed in previous works by the authors to study black hole entropy in the new proposal put forth by Engle, Noui, and Perez. Specifically, we give the generating functions relevant for the computation of the entropy and use them to derive its asymptotic behavior, including the value of the Immirzi parameter and the coefficient of the logarithmic correction.
Entropy production and information fluctuations along quantum trajectories
2013
Employing the stochastic wave function method, we study quantum features of stochastic entropy production in nonequilibrium processes of open systems. It is demonstarted that continuous measurements on the environment introduce an additional, non-thermal contribution to the entropy flux, which is shown to be a direct consequence of quantum fluctuations. These features lead to a quantum definition of single trajectory entropy contributions, which accounts for the difference between classical and quantum trajectories and results in a quantum correction to the standard form of the integral fluctuation theorem.
Mutual information and spontaneous symmetry breaking
2015
We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g. at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly non trivial. We prove this result in general, by considering the quantum mutual …
Entropic trade-off relations for quantum operations
2013
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of the dynamical matrix describes the degree of decoherence introduced by the map, while the entropy of the superoperator characterizes the a priori knowledge of the receiver of the outcome of a quantum channel Phi. We prove that for any map acting on a N--dimensional quantum system the sum of both entropies is not smaller than ln N. For any bistochastic map this lower bound reads 2 ln N. We investigate also the corresponding R\'enyi entropies, providing an …
New structures in the theory of the laser model. II. Microscopic dynamics and a nonequilibrium entropy principle
1998
In a recent article, Alli and Sewell [J. Math. Phys. 36, 5598 (1995)] formulated a new version of the Dicke-Hepp-Lieb laser model in terms of quantum dynamical semigroups, and thereby extended the macroscopic picture of the model. In the present article, we complement that picture with a corresponding microscopic one, which carries the following new results. (a) The local microscopic dynamics of the model is piloted by the classical, macroscopic field, generated by the collective action of its components; (b) the global state of the system carries no correlations between its constituent atoms after transient effects have died out; and (c) in the latter situation, the state of the system at …
Thermodynamics based on the principle of least abbreviated action: Entropy production in a network of coupled oscillators
2006
We present some novel thermodynamic ideas based on the Maupertuis principle. By considering Hamiltonians written in terms of appropriate action-angle variables we show that thermal states can be characterized by the action variables and by their evolution in time when the system is nonintegrable. We propose dynamical definitions for the equilibrium temperature and entropy as well as an expression for the nonequilibrium entropy valid for isolated systems with many degrees of freedom. This entropy is shown to increase in the relaxation to equilibrium of macroscopic systems with short-range interactions, which constitutes a dynamical justification of the Second Law of Thermodynamics. Several e…