arXiv subjects

Qiuping A. Wang

Publications and source records attributed to Qiuping A. Wang.

At least 37 records · Page 2Linked to original sources

arXiv2008

Generalized measurement of uncertainty and the maximizable entropy

For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation, bar(x)=sum_(i)g(p_i)x_i, and the expression of dI, we can find the concrete forms of the maximizable entropies for any given probability distribution function, where g(p_i) may have different forms for different statistics which includes the extensive and nonextensive statistics.

cond-mat.stat-mech↗

arXiv2008

Inherent correlations between thermodynamics and statistic physics in extensive and nonextensive systems

With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistic physics. These relations are proved through the MaxEnt approach once again. It is found that for a reversible isothermal process, the information contained in the first and second laws of thermodynamics and the MaxEnt approach is equivalent. Moreover, these relations are used to derive the probability distribution functions in nonextensive and extensive statistics and calculate the generalized forces of some interesting systems. The results obtained are of universal significance.

cond-mat.stat-mech↗

arXiv2008

Maximizable informational entropy as measure of probabilistic uncertainty

In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d - ) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized virtual work principle =0 leading to maximum entropy d(I-beta* )=0. This paper presents an analytical investigation of this maximizable entropy for several distributions such as stretched exponential distribution, kappa-exponential distribution and Cauchy distribution.

cond-mat.stat-mech↗

arXiv2008

A mathematical structure for the generalization of the conventional algebra

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from mathematical point of view, any bijective function can be used in principle to formulate an algebra in which the conventional algebraic rules are generalized.

cond-mat.stat-mech↗

arXiv2008

Seeing maximum entropy from the principle of virtual work

We propose an extension of the principle of virtual work of mechanics to random dynamics of mechanical systems. The total virtual work of the interacting forces and inertial forces on every particle of the system is calculated by considering the motion of each particle. Then according to the principle of Lagrange-d'Alembert for dynamical equilibrium, the vanishing ensemble average of the virtual work gives rise to the thermodynamic equilibrium state with maximization of thermodynamic entropy. This approach establishes a close relationship between the maximum entropy approach for statistical mechanics and a fundamental principle of mechanics, and constitutes an attempt to give the maximum entropy approach, considered by many as only an inference principle based on the subjectivity of probability and entropy, the status of fundamental physics law.

cond-mat.stat-mech↗

arXiv2008

Probability distribution and entropy as a measure of uncertainty

The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability distribution of a random variable x by a variational relationship, a definition underlying the maximization of entropy for corresponding distribution.

cond-mat.stat-mech↗

arXiv2007

From virtual work principle to maximum entropy for nonequilibrium system

After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this paper another application of the principle to thermodynamic systems out of equilibrium. Unlike the justification of maximum path entropy for the motion trajectories during a period of time, this work is on the maximum of the entropy defined as a measure of the momentary dynamical uncertainty as a function of the probability distribution over the microstates of the system at any given moment.

cond-mat.stat-mech↗

arXiv2007

From virtual work principle to least action principle for stochastic dynamics

After the justification of the maximum entropy principle for equilibrium mechanical system from the principle of virtual work, i.e., the virtual work of microscopic forces on the elements of a mechanical system vanishes in thermodynamic equilibrium, we present in this paper an application of the same principle to dynamical systems out of equilibrium. The aim of this work is to justify a least action principle and the concurrent maximum path entropy principle for nonequilibrium thermodynamic systems.

cond-mat.stat-mech↗

arXiv2007

Incomplete normalization of probability on multifractals

This work is an extension of the incomplete probability theory from the simple case of monofractals previously studied to the more general case of multifractals which can occur in the phase space without equiprobable partition.

cond-mat.stat-mech↗

arXiv2006

On different $q$-systems in nonextensive thermostatistics

It is known that the nonextensive statistics was originally formulated for the systems composed of subsystems having same $q$. In this paper, the existence of composite system with different $q$ subsystems is investigated by fitting the power law degree distribution of air networks with $q$-exponential distribution. Then a possible extension the nonextensive statistics to different $q$ systems is provided on the basis of an entropy nonadditivity rule and an unnormalized expectation of energy.

cond-mat.stat-mech↗

arXiv2006

A composition of different $q$ nonextensive systems with the normalized expectation based on escort probability

This is a study of composition rule and temperature definition for nonextensive systems containing different $q$ subsystems. The physical meaning of the multiplier $β$ associated with the energy expectation in the optimization of Tsallis entropy is investigated for the formalism with normalized expectation given by escort probability. This study is carried out for two possible cases: the case of the approximation of additive energy; and the case of nonadditive energy prescribed by an entropy composition rule for different $q$ systems.

cond-mat.stat-mech↗

arXiv2006

How to fit the degree distribution of the air network?

We investigate three different approaches for fitting the degree distributions of China-, US- and the composite China+US air network, in order to reveal the nature of such distributions and the potential theoretical background on which they are based. Our first approach is the fitting with q-statistics probability distribution, done separately in two regimes. This yields acceptable outcomes but generates two sets of fitting parameters. The second approach is an entire fitting to all data points with the formula proposed by Tsallis et al. So far, this trial is not able to produce consistent results. In the third approach, we fit the data with two composite distributions which may lack theoretical support for the moment.

physics.soc-ph↗

arXiv2005

Ab initio investigation of lattice dynamics of fluoride scheelite LiYF4

We report on the phonon dynamics of LiYF4 obtained by direct method using first principle calculations. The agreement between experimental and calculated modes is satisfactory. An inversion between two Raman active modes is noticed compared to inelastic neutron scattering and Raman measurements. The atomic displacements corresponding to these modes are discussed. Multiple inversions between Raman and infrared active groups are present above 360 cm-1. The total and partial phonon density of state is also calculated and analyzed.

cond-mat.mtrl-sci↗

arXiv2005

Non quantum uncertainty relations of stochastic dynamics

First we describe briefly an information-action method for the study of stochastic dynamics of hamiltonian systems perturbed by thermal noise and chaotic instability. It is shown that, for the ensemble of possible paths between two configuration points, the action principle acquires a statistical form $<δA>=0$. The main objective of this paper is to prove that, via this information-action description, some quantum like uncertainty relations such as $<ΔA>\geq\frac{1}{\sqrt{2}η}$ for action, $<Δx><ΔP>\geq\frac{1}η$ for position and momentum, and $<ΔH><Δt>\geq\frac{1}{\sqrt{2}η}$ for hamiltonian and time, can arise for stochastic dynamics of classical hamiltonian systems. A corresponding commutation relation can also be found. These relations describe, through action or its conjugate variables, the fluctuation of stochastic dynamics due to random perturbation characterized by the parameter $η$.

cond-mat.stat-mech↗

arXiv2004

A mathematical method for irregular hamiltonian systems

We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular) noise and chaotic motion. The random effect is taken into account via the uncertainty of irregular dynamic process produced in this way. This uncertainty due to different paths between two phase points is measured by a path information which is maximized in connection with the action defined originally for the unperturbed regular hamiltonian systems. The obtained transition probability depends exponentially on this action. The usefulness of this information method has been demonstrated by the derivation of diffusion laws without the usual assumptions. In this work, some essential mathematical aspects of this irregular dynamics is reviewed. It is emphasized that the classical action principle for single least action path is no more valid and the formalism of classical mechanics for regular hamiltonian systems is no more exact for irregular hamiltonian dynamics. There is violation of the fundamental laws of mechanics by randomly perturbed hamiltonian systems. However, the action principle is always present for the ensemble of paths through the average action. This average action principle leads to a formalism of stochastic mechanics in which, in spite of the violation of fundamental laws, the mathematical form of classical mechanics can be recovered by a consideration of the statistical averaging of the dynamics.

cond-mat.stat-mech↗

arXiv2004

Diffusion laws, information and action principle

This is an attempt to address diffusion phenomena from the point of view of information theory. We imagine a regular hamiltonian system under the random perturbation of thermal (molecular) noise and chaotic instability. The irregularity of the random process produced in this way is taken into account via the dynamic uncertainty measured by a path information associated with different transition paths between two points in phase space. According to the result of our previous work, this dynamic system maximizes this uncertainty in order to follow the action principle of mechanics. In this work, this methodology is applied to particle diffusion in external potential field. By using the exponential probability distribution of action (least action distribution) yielded by maximum path information, a derivation of Fokker-Planck equation, Fick's laws and Ohm's law for normal diffusion is given without additional assumptions about the nature of the process. This result suggests that, for irregular dynamics, the method of maximum path information, instead of the least action principle for regular dynamics, should be used in order to obtain the correct occurring probability of different paths of transport. Nevertheless, the action principle is present in this formalism of stochastic mechanics because the average action has a stationary associated with the dynamic uncertainty. The limits of validity of this work is discussed.

cond-mat.stat-mech↗

arXiv2004

Maximum entropy change and least action principle for nonequilibrium systems

A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path probability distribution in exponentials of action. This means that the most probable paths are just the paths of least action. This distribution naturally leads to important laws of normal diffusion. A conclusion of this work is that, for probabilistic mechanics or irregular dynamics, the principle of maximization of path information is equivalent to the least action principle for regular dynamics. We also show that an average path information between the initial phase volume and the final phase volume can be related to the entropy change defined with natural invariant measure of dynamic system. Hence the principles of least action and maximum path information suggest the maximum entropy change. This result is used for some chaotic systems evolving in fractal phase space in order to derive their invariant measures.

cond-mat.stat-mech↗

arXiv2004

Maximum path information and the principle of least action for chaotic system

A path information is defined in connection with the different possible paths of chaotic system moving in its phase space between two cells. On the basis of the assumption that the paths are differentiated by their actions, we show that the maximum path information leads to a path probability distribution as a function of action from which the well known transition probability of Brownian motion can be easily derived. An interesting result is that the most probable paths are just the paths of least action. This suggests that the principle of least action, in a probabilistic situation, is equivalent to the principle of maximization of information or uncertainty associated with the probability distribution.

cond-mat.stat-mech↗