We study a 1-dimensional AKLT spin chain, consisting of spins S in the bulk and S/2 at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension (S + 1) 2 . This subspace is des...

Certain fluctuations in particle number, n, at fixed total energy, E, lead exactly to a cut-power law distribution in the one-particle energy, ω, via the induced fluctuations in the phase-space volume ratio, Ωn(E − ω)/Ωn(E) = (1 − ω/E). The only parameters are 1/T = 〈β〉 = 〈n〉/E and q = 1−1/〈n〉+∆n2/〈n〉2. For the binomial distribution of n one obtains q = 1−1/k, for the negative binomial q = 1+1/...

Highly excited many-particle states in quantum systems (nuclei, atoms, quantum dots, spin systems, quantum computers) can be " chaotic " superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is a result of the very high energy level density of many-body states which can be easily mixed by a residual interaction between particles. We consider the...

We show that the relative entropy, S(rel) identical with Sigma(p(T)) ln(p(T)/p(M)), provides a fundamental and unifying framework for multiscale analysis and for inverse molecular-thermodynamic problems involving optimization of a model system (M) to reproduce the properties of a target one (T). We demonstrate that the relative entropy serves as a generating function for principles in variation...

We measured entropy and symbolic diversity of texts written in English and Spanish. We included texts by Literature Nobel laureates and other famous authors. We formed four groups of texts according to the combinations of language used and the author's Literature Nobel Prize condition. Entropy, symbol diversity and symbol frequency profiles were compared for these four groups. We also built a s...

Let f be an endomorphism of an irreducible sofic system S, where S has entropy Iog)t. The degree of f is the number d such that f is d to 1 almost everywhere. Then d divides a power of the greatest common divisor of the nonleading coefficients of the minimal polynomial of )t. Also, f multiplies the natural measure on unstable sets of generic points by a positive unit of the ring generated by 1/...

Based on a model of quantum measurement we derive an estimate for the external measurement-time. Some interesting consequences will be analyzed. Keywords: Quantum Entropy, Energy, Measurement, Time MSC 2000 codes: 94A17, 81P15 Entropy 2006, 8, 182-187 183 1 Introduction Given an apparatus or memory A, a system S and the environment E , the measurement process M can be represented by the followi...

The identification of a causal-connection scale motivates us to propose a new covariant bound on entropy within a generic space-like region. This “causal entropy bound”, scaling as √ EV , and thus lying around the geometric mean of Bekenstein’s S/ER and holographic S/A bounds, is checked in various “critical” situations. In the case of limited gravity, Bekenstein’s bound is the strongest while ...

We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincaré inequalities for such functions. This leads naturally to the concept of f -divergence and, in particular, relative entropy for s-concave and log concave functions. We establish their basic properties, among them the affine invariant valua...

By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy S of a finite-dimensional system around a non-degenerate critical point of its potential energy V . We compare S with the entropy of a quantum or thermal system with effective potential Veff . We examine conditions, up to first order in perturbation theory, under which these entrop...