Fluctuations of the partial filling factors in competitive RSA from binary mixtures

Competitive random sequential adsorption on a line from a binary mix of incident particles is studied using both an analytic recursive approach and Monte Carlo simulations. We find a strong correlation between the small and the large particle distributions so that while both partial contributions to the fill factor fluctuate widely, the variance of the total fill factor remains relatively small. The variances of partial contributions themselves are quite different between the smaller and the larger particles, with the larger particle distribution being more correlated. The disparity in fluctuations of partial fill factors increases with the particle size ratio. The additional variance in the partial contribution of smaller particle originates from the fluctuations in the size of gaps between larger particles. We discuss the implications of our results to semiconductor high-energy gamma detectors where the detector energy resolution is controlled by correlations in the cascade energy branching process.Comment: 19 pages, 8 figure

A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations

We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) for the purpose of calculating the Renyi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analogue to the density of states for Stochastic Series Expansion QMC allowing a direct calculation of Renyi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, 2D transverse field Ising model, and 3D Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.Comment: 9 pages, 7 figure

A Classical Bound on Quantum Entropy

A classical upper bound for quantum entropy is identified and illustrated, $0\leq S_q \leq \ln (e \sigma^2 / 2\hbar)$, involving the variance $\sigma^2$ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.Comment: Latex2e, 7 pages, publication versio

A step beyond Tsallis and Renyi entropies

Tsallis and R\'{e}nyi entropy measures are two possible different generalizations of the Boltzmann-Gibbs entropy (or Shannon's information) but are not generalizations of each others. It is however the Sharma-Mittal measure, which was already defined in 1975 (B.D. Sharma, D.P. Mittal, J.Math.Sci \textbf{10}, 28) and which received attention only recently as an application in statistical mechanics (T.D. Frank & A. Daffertshofer, Physica A \textbf{285}, 351 & T.D. Frank, A.R. Plastino, Eur. Phys. J., B \textbf{30}, 543-549) that provides one possible unification. We will show how this generalization that unifies R\'{e}nyi and Tsallis entropy in a coherent picture naturally comes into being if the q-formalism of generalized logarithm and exponential functions is used, how together with Sharma-Mittal's measure another possible extension emerges which however does not obey a pseudo-additive law and lacks of other properties relevant for a generalized thermostatistics, and how the relation between all these information measures is best understood when described in terms of a particular logarithmic Kolmogorov-Nagumo average

Information theoretical properties of Tsallis entropies

A chain rule and a subadditivity for the entropy of type $\beta$, which is one of the nonadditive entropies, were derived by Z.Dar\'oczy. In this paper, we study the further relations among Tsallis type entropies which are typical nonadditive entropies. The chain rule is generalized by showing it for Tsallis relative entropy and the nonadditive entropy. We show some inequalities related to Tsallis entropies, especially the strong subadditivity for Tsallis type entropies and the subadditivity for the nonadditive entropies. The subadditivity and the strong subadditivity naturally lead to define Tsallis mutual entropy and Tsallis conditional mutual entropy, respectively, and then we show again chain rules for Tsallis mutual entropies. We give properties of entropic distances in terms of Tsallis entropies. Finally we show parametrically extended results based on information theory.Comment: The subsection on data processing inequality was deleted. Some typo's were modifie

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

5 pages, 1 figur

Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems

We present a general scheme for the calculation of the Renyi entropy of a subsystem in quantum many-body models that can be efficiently simulated via quantum Monte Carlo. When the simulation is performed at very low temperature, the above approach delivers the entanglement Renyi entropy of the subsystem, and it allows to explore the crossover to the thermal Renyi entropy as the temperature is increased. We implement this scheme explicitly within the Stochastic Series expansion as well as within path-integral Monte Carlo, and apply it to quantum spin and quantum rotor models. In the case of quantum spins, we show that relevant models in two dimensions with reduced symmetry (XX model or hardcore bosons, transverse-field Ising model at the quantum critical point) exhibit an area law for the scaling of the entanglement entropy.Comment: 5+1 pages, 4+1 figure

Diàleg sobre el llenguatge del Llibre de la Naturalesa

Aquesta traducció al català del tercer diàleg de Rényi completa la dels dos anteriors, publicats en el Butlletí [25]. Tracta, com el títol indica, del «llenguatge del Llibre de la Naturalesa». Els protagonistes són Galileu Galilei, Caterina Niccolini i Evangelista Torricelli. Els temes que s'hi tracten són diversos. El diàleg que inicia el text —entre Galileu i Torricelli— tracta de les raons que han dut Galileu a enfrontar-se a la Inquisició —la defensa de la llibertat de pensament i de recerca en la filosofia de la naturalesa. En la resta del diàleg —entre Galileu i la Sra. Niccolini— les qüestions són diverses: des de què cal entendre com a mètode científic fins a quin és el llenguatge de la naturalesa —la matemàtica— amb les contradiccions que això comporta quan topem amb l'atzar i la matemàtica de l'atzar, i amb l'infinit. És un text —com els altres dos— d'una elegància i claredat magistrals. Totes les notes del text —tant les històriques com les metodològiques— són notes aclaridores del traductor que no es troben a l'original de Rényi. A l'apèndix, oferim una cronologia de la vida de Galileu.This is the translation into catalan of the third of Rényi’s dialogues, and completes that of the two previous ones, published in this Butlletí in 2002 and 2004. As the title indicates, it deals with the language of the Book of Nature. The characters are Galileo Galilei, Caterina Niccolini, and Evangelista Torricelli. It touches on several, diverse topics. The initial dialogue—between Galileo and Torricelli—deals with the reasons that have lead Galileo to face the Inquisition— the defence of freedom of thought and of research on the philosophy of nature. The rest of the dialogue—between Galileo and Mrs. Niccolini—deals with several topics: from what should be understood as scientific method to which is the language of nature—mathematics—together with the difficulties that this entails when we bump into randomness and the mathematics of randomness and with the infinite. Like the other two dialogues, this text is masterfully clear and elegant. Many notes by the translator present all the characters mentioned in the dialogue and the historical circumstances that justify their appearance, and explain other historical and methodological points. A chronology of Galileo’s life is included as an Appendix