arXiv subjects

Q. A. Wang

Publications and source records attributed to Q. A. Wang.

At least 19 recordsLinked to original sources

arXiv2022

Study of a measure of efficiency as a tool for applying the principle of least effort to the derivation of the Zipf and the Pareto laws

The principle of least effort is believed to be a universal rule for living systems. Its application to the derivation of the power law probability distributions of living systems has long been challenging. Recently, a measure of efficiency was proposed as a tool of deriving Zipf s and Pareto s laws directly from the principle of least effort. The present work is a further investigation of this efficiency measure from a mathematical point of view. The aim is to get further insight into its properties and usefulness as a metric of performance. We address some key mathematical properties of this efficiency such as its sign, uniqueness and robustness. We also look at the relationship between this measure and other properties of the system of interest such as inequality and uncertainty, by introducing a new method for calculating non-negative continuous entropy.

math.PR↗

arXiv2014

Rank-frequency relation for Chinese characters

We show that the Zipf's law for Chinese characters perfectly holds for sufficiently short texts (few thousand different characters). The scenario of its validity is similar to the Zipf's law for words in short English texts. For long Chinese texts (or for mixtures of short Chinese texts), rank-frequency relations for Chinese characters display a two-layer, hierarchic structure that combines a Zipfian power-law regime for frequent characters (first layer) with an exponential-like regime for less frequent characters (second layer). For these two layers we provide different (though related) theoretical descriptions that include the range of low-frequency characters (hapax legomena). The comparative analysis of rank-frequency relations for Chinese characters versus English words illustrates the extent to which the characters play for Chinese writers the same role as the words for those writing within alphabetical systems.

cs.CL↗

arXiv2013

Long division unites - long union divides, a model for social network evolution

A remarkable phenomenon in the time evolution of many networks such as cultural, political, national and economic systems, is the recurrent transition between the states of union and division of nodes. In this work, we propose a phenomenological modeling, inspired by the maxim "long union divides and long division unites", in order to investigate the evolutionary characters of these networks composed of the entities whose behaviors are dominated by these two events. The nodes are endowed with quantities such as identity, ingredient, richness (power), openness (connections), age, distance, interaction etc. which determine collectively the evolution in a probabilistic way. Depending on a tunable parameter, the time evolution of this model is mainly an alternative domination of union or division state, with a possible state of final union dominated by one single node.

physics.soc-ph↗

arXiv2013

Numerical study of path probability for stochastic motion of non dissipative systems

The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces in addition to Gaussian distributed random displacements. In the presence of dissipative forces, application of this ideal model requires that the dissipated energy is small with respect to the variation (work) of the conservative forces. The sample paths are sufficiently smooth space-time tubes with suitable width allowing correct evaluation of position, velocity, energy and action of each tube. It is found that the path probability decays exponentially with increasing action of the sample paths. The decay rate increases with decreasing Gaussian randomness.

cond-mat.stat-mech↗

arXiv2013

Path probability distribution of stochastic motion of non dissipative systems: a classical analog of Feynman factor of path integral

We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model of simulation is a one-dimensional particle subject to conservative force and Gaussian random displacement. The probability that a sample path between two fixed points is taken is computed from the number of particles moving along this path, an output of the simulation, devided by the total number of particles arriving at the final point. It is found that the path probability decays exponentially with increasing action of the sample paths. The decay rate increases with decreasing randomness. This result supports the existence of a classical analog of the Feynman factor in the path integral formulation of quantum mechanics for Hamiltonian systems.

cond-mat.stat-mech↗

arXiv2013

Adaptive machine and its thermodynamic costs

We study the minimal thermodynamically consistent model for an adaptive machine that transfers particles from a higher chemical potential reservoir to a lower one. This model describes essentials of the inhomogeneous catalysis. It is supposed to function with the maximal current under uncertain chemical potentials: if they change, the machine tunes its own structure fitting it to the maximal current under new conditions. This adaptation is possible under two limitations. (i) The degree of freedom that controls the machine's structure has to have a stored energy (described via a negative temperature). The origin of this result is traced back to the Le Chatelier principle. (ii) The machine has to malfunction at a constant environment due to structural fluctuations, whose relative magnitude is controlled solely by the stored energy. We argue that several features of the adaptive machine are similar to those of living organisms (energy storage, aging).

cond-mat.stat-mech↗

arXiv2013

Explaining Zipf's Law via Mental Lexicon

The Zipf's law is the major regularity of statistical linguistics that served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that the Zipf's law -- together with its applicability for a single text and its generalizations to high and low frequencies including hapax legomena -- can be derived from assuming that the words are drawn into the text with random probabilities. Their apriori density relates, via the Bayesian statistics, to general features of the mental lexicon of the author who produced the text.

physics.data-an↗

arXiv2010

Study of the Urban Road Networks of Le Mans

An urban road network of Le Mans in France is analyzed. Some topological properties of network are investigated, such as degree distribution, clustering coefficient, diameter, and characteristic path length. These results suggest that our network is a "small- world" network with short average shortest path and large clustering coefficient. Furthermore, double power-law distribution is found in degree distribution which is distinct from the single power-law and a novel degree distribution function is also given. Some analysis on this function extend the comprehension of the origination of the double power-law distribution widely dispersed in nature.

physics.soc-ph↗

arXiv2009

The q-nonadditivity of nonextensive statistics is not a true physical property

This is a note showing that, contrary to our lasting belief, the nonadditivity X(1+2)=X(1)+X(2)+αX(1)X(2) is not a true physical property. αin this expression cannot be unique for a given system. It unavoidably depends on how one mathematically divides the system and cannot be used to characterize nonadditivity. As a matter of fact, its use is mathematically inconsistent.

cond-mat.stat-mech↗

arXiv2008

A nonextensive approach to Bose-Einstein condensation of trapped interacting boson gas

In the Bose-Einstein condensation of interacting atoms or molecules such as 87Rb, 23Na and 7Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy Uq and the particle number Nq of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature Tcq is derived versus Tc given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q ~ 0.1 for 87Rb atomic gas, q ~ 0.95 for 7Li and q ~ 0.62 for 23Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory.

cond-mat.stat-mech↗

arXiv2008

Understanding heavy fermion from generalized statistics

Heavy electrons in superconducting materials are widely studied with the Kondo lattice t-J model. Numerical results have shown that the Fermi surface of these correlated particles undergoes a flattening effect according to the coupling degree J. This behaviour is not easy to understand from the theoretical point of view within standard Fermi-Dirac statistics and non-standard theories such as fractional exclusion statistics for anyons and Tsallis nonextensive statistics. The present work is an attempt to account for the heavy electron distribution within incomplete statistics (IS) which is developed for complex systems with interactions which make the statistics incomplete such that sum_i p_i^q=1. The parameter q, when different from unity, characterizes the incompleteness of the statistics. It is shown that the correlated electrons can be described with the help of IS with q related to the coupling constant J in the context of Kondo model

cond-mat.stat-mech↗

arXiv2007

Stochastic action principle and maximum entropy

A stochastic action principle for stochastic dynamics is revisited. We present first numerical diffusion experiments showing that the diffusion path probability depend exponentially on average Lagrangian action. This result is then used to derive an uncertainty measure defined in a way mimicking the heat or entropy in the first law of thermodynamics. It is shown that the path uncertainty (or path entropy) can be measured by the Shannon information and that the maximum entropy principle and the least action principle of classical mechanics can be unified into a concise form. It is argued that this action principle, hence the maximum entropy principle, is simply a consequence of the mechanical equilibrium condition extended to the case of stochastic dynamics.

cond-mat.stat-mech↗

arXiv2004

Applying incomplete statistics to nonextensive systems with different $q$ indices

The nonextensive statistics based on the $q$-entropy $S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems in which the $q$ value is uniformly distributed. For the systems containing different $q$'s, the applicability of the theory is still a matter of investigation. The difficulty is that the class of systems to which the theory can be applied is actually limited by the usual nonadditivity rule of entropy which is no more valid when the systems contain non uniform distribution of $q$ values. In this paper, within the framework of the so called incomplete information theory, we propose a more general nonadditivity rule of entropy prescribed by the zeroth law of thermodynamics. This new nonadditivity generalizes in a simple way the usual one and can be proved to lead uniquely to the $q$-entropy.

cond-mat.stat-mech↗

arXiv2004

Action principle and Jaynes' guess method

A path information is defined in connection with the probability distribution of paths of nonequilibrium hamiltonian systems moving in phase space from an initial cell to different final cells. On the basis of the assumption that these paths are physically characterized by their action, we show that the maximum path information leads to an exponential probability distribution of action which implies that the most probable paths are just the paths of stationary action. We also show that the averaged (over initial conditions) path information between an initial cell and all the possible final cells can be related to the entropy change defined with natural invariant measures for dynamical systems. Hence the principle of maximum path information suggests maximum entropy and entropy change which, in other words, is just an application of the action principle of classical mechanics to the cases of stochastic or instable dynamics.

cond-mat.stat-mech↗

arXiv2004

Fourier's law and maximum path information

By using a path information defined for the measure of the uncertainty of instable dynamics, a theoretical derivation of Fourier's law of heat conduction is given on the basis of maximum information method associated with the principle of least action.

cond-mat.stat-mech↗

arXiv2004

Fractal geometry, information growth and nonextensive thermodynamics

This is a study of the information evolution of complex systems by geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness of the state number counting at any scale on fractal support, the incomplete normalization $\sum_ip_i^q=1$ is applied throughout the paper, where $q$ is the fractal dimension divided by the dimension of the smooth Euclidean space in which the fractal structure of the phase space is embedded. It is shown that the information growth is nonadditive and is proportional to the trace-form $\sum_ip_i-\sum_ip_i^q$ which can be connected to several nonadditive entropies. This information growth can be extremized to give power law distributions for these non-equilibrium systems. It can also be used for the study of the thermodynamics derived from Tsallis entropy for nonadditive systems which contain subsystems each having its own $q$. It is argued that, within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can be preserved.

cond-mat.stat-mech↗

arXiv2003

Measuring information growth in fractal phase space

We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness, at any scale, of the information calculation in fractal support, the incomplete normalization $\sum_ip_i^q=1$ is applied throughout the paper. It is shown that the information growth is nonadditive and is proportional to the trace-form $\sum_ip_i-\sum_ip_i^q$ so that it can be connected to several nonadditive entropies. This information growth can be extremized to give, for non-equilibrium systems, power law distributions of evolving stationary state which may be called ``maximum entropic evolution''.

cond-mat.stat-mech↗

arXiv2003

Generalized algebra within a nonextensive statistics

By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g., associativity, commutativity and existence of neutral elements. On the contrary, the distributivity law and the opposite element is no more universal within the generalized algebra.

math-ph↗