arXiv subjects

Qiuping A. Wang

Publications and source records attributed to Qiuping A. Wang.

At least 19 recordsLinked to original sources

arXiv2025

Supervised and unsupervised learning with numerical computation for the Wolfram cellular automata

The local rules of Wolfram cellular automata with one-dimensional three-cell neighborhoods are represented by eight-bit binary that encode deterministic update rules. These automata are widely utilized to investigate self-organization phenomena and the dynamics of complex systems. In this work, we employ numerical simulations and computational methods to investigate the asymptotic density and dynamical evolution mechanisms in Wolfram automata. We apply both supervised and unsupervised learning methods to identify the configurations associated with different Wolfram rules. Furthermore, we explore alternative initial conditions under which certain Wolfram rules generate similar fractal patterns over time, even when starting from a single active site. Our results reveal the relationship between the asymptotic density and the initial density of selected rules. The supervised learning methods effectively identify the configurations of various Wolfram rules, while unsupervised methods like principal component analysis and autoencoders can approximately cluster configurations of different Wolfram rules into distinct groups, yielding results that align well with simulated density outputs.

physics.comp-ph↗

arXiv2021

A stochastic least action principle applied in the description of black swan events

In this paper we present a formulation of the stochastic least action principle (SAP) to encompass random movements with black swan events (of non dissipative systems) in terms of heavy tailed distributions. The black swan events are rare and drastic events, such as earthquakes and financial crisis. It has been observed that the Tsallis entropy suits well in the description of the black swan events rather than the Shannon-Boltzman-Gibbs entropy, which is intrinsically related to the fact that black swan events of physical systems are proportional to non-local correlations. As a consequence, we could assess the validity of the path probability distribution obtained using the non-additive Tsallis entropy.

cond-mat.stat-mech↗

arXiv2021

Principle of least effort vs maximum efficiency: deriving Zipf-Pareto laws

This paper provides a derivation of Zipf-Pareto laws directly from the principle of least effort. A probabilistic functional of efficiency is introduced as the consequence of an extension of the nonadditivity of the efficiency of thermodynamic engine to a large number of living agents assimilated to engines, all randomly distributed over their output. Application of the maximum calculus to this efficiency yields the Zipf-Pareto laws.

physics.soc-ph↗

arXiv2020

From Random Motion of Hamiltonian Systems to Boltzmann H Theorem and Second Law of Thermodynamics -- a Pathway by Path Probability

A numerical experiment of ideal stochastic motion of a particle subject to conservative forces and Gaussian noise reveals that the path probability depends exponentially on action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian-Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory, Liouville theorem of conservation of phase density distribution must be modified to allow time evolution of phase density and consequently the Boltzmann H theorem. We argue that the gap between the regular Newtonian dynamics and the random dynamics was not considered in the criticisms of the H theorem.

cond-mat.stat-mech↗

arXiv2015

Composition of Fractals

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function of the component dimensions. But in the case of the compositions including component multifractals, the composite dimension cannot be expressed as explicit function of component dimensions and can only be solved numerically. An application of fractal composition to a physics problem within the incomplete statistics is discussed.

math.MG↗

arXiv2015

Back to Maupertuis' least action principle for dissipative systems: not all motions in Nature are most energy economical

It is shown that an oldest form of variational calculus of mechanics, the Maupertuis least action principle, can be used as a simple and powerful approach for the formulation of the variational principle for damped motions, allowing a simple derivation of the Lagrangian mechanics for any dissipative systems and an a connection of the optimization of energy dissipation to the least action principles. On this basis, it is shown that not all motions of classical mechanics obey the rule of least energy dissipation or follow the path of least resistance, and that the least action is equivalent to least dissipation for two kinds of motions : all stationary motions with constant velocity and all motions damped by Stokes drag.

cond-mat.stat-mech↗

arXiv2015

Is it possible to formulate least action principle for dissipative systems?

A longstanding open question in classical mechanics is to formulate the least action principle for dissipative systems. In this work, we give a general formulation of this principle by considering a whole conservative system including the damped moving body and its environment receiving the dissipated energy. This composite system has the conservative Hamiltonian $H=K_1+V_1+H_2$ where $K_1$ is the kinetic energy of the moving body, $V_1$ its potential energy and $H_2$ the energy of the environment. The Lagrangian can be derived by using the usual Legendre transformation $L=2K_1+2K_2-H$ where $K_2$ is the total kinetic energy of the environment. An equivalent expression of this Lagrangian is $L=K_1-V_1-E_d$ where $E_d$ is the energy dissipated by the friction from the moving body into the environment from the beginning of the motion. The usual variation calculus of least action leads to the correct equation of the damped motion. We also show that this general formulation is a natural consequence of the virtual work principle.

cond-mat.stat-mech↗

arXiv2014

Least action principle and stochastic motion : a generic derivation of path probability

This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the case of non dissipative limit, the action is the usual one in mechanics in accordance with the previous result of numerical simulation of random motion. In the case of dissipative motion, the action in the exponent of the exponential probability is just the one proposed in a previous work (Q.A. Wang, R. Wang, arXiv:1201.6309), an action defined for the total system including the moving system and its environment receiving the dissipated energy. In both cases, the result implies that the most probable paths are the paths of least action which, in the limit of vanishing randomness, become the regular paths minimizing the action.

cond-mat.stat-mech↗

arXiv2013

Fractional Dynamics, Tiling Equilibrium states and Riemann's zeta function

Il is argued that the generalisation of the mechanical principles to other variables than localisation, velocity and momentum leads to the laws of generalized dynamics under the condition of continuous and derivable space time. However, when the fractality arises, the mechanics principles may no more be extended especially because the time and space singularity appears on the boundary and creates curvature. There is no more equilibrium state, but only a horizon which might play a same role as equilibrium but does not close the problem - especially the problem of the invariance of the energy - which requires two complementary factors: a first one related to the closure in the dimensional space, and the second to scan dissymmetry stemming from the default of tilling the space time. A new discreet time arises from fractality. It leads irreversible thermodynamic properties. Space and time singularities lead to the relation between the above mentioned problematic and the Riemann zeta functions as well as its zeros.

cond-mat.stat-mech↗

arXiv2013

The extrema of an action principle for dissipative mechanical systems

A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties persist about the appropriate variational calculus and the nature (maxima, minima and inflection) of the stationary action. The aim of this work is to make numerical simulation of damped motion and to compare the actions of different paths in order to get evidence of the existence and the nature of stationary action. The model is a small particle subject to conservative and friction forces. Two conservative forces and three friction forces are considered. The comparison of the actions of the perturbed paths with that of the Newtonian path reveals the existence of extrema of action which are minima for zero or very weak friction and shift to maxima when the motion is overdamped. In the intermediate case, the action of the Newtonian path is neither least nor most, meaning that the extreme feature of the Newtonian path is lost. In this situation, however, no reliable evidence of stationary action can be found from the simulation result.

physics.class-ph↗

arXiv2012

Casimir effect of an ideal Bose gas trapped in a generic power-law potential

The Casimir effect of an ideal Bose gas trapped in a generic power-law potential and confined between two slabs with Dirichlet, Neumann, and periodic boundary conditions is investigated systematically, based on the grand potential of the ideal Bose gas, the Casimir potential and force are calculated. The scaling function is obtained and discussed. The special cases of free and harmonic potentials are also discussed. It is found that when T Tc, the Casimir force is an exponential decay function; and when T>>Tc, the Casimir force vanishes.

cond-mat.stat-mech↗

arXiv2011

Universal scaling in sports ranking

Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth. Herewith, we study a specific kind, sports ranking systems in which players' scores and prize money are calculated based on their performances in attending various tournaments. A typical example is tennis. It is found that the distributions of both scores and prize money follow universal power laws, with exponents nearly identical for most sports fields. In order to understand the origin of this universal scaling we focus on the tennis ranking systems. By checking the data we find that, for any pair of players, the probability that the higher-ranked player will top the lower-ranked opponent is proportional to the rank difference between the pair. Such a dependence can be well fitted to a sigmoidal function. By using this feature, we propose a simple toy model which can simulate the competition of players in different tournaments. The simulations yield results consistent with the empirical findings. Extensive studies indicate the model is robust with respect to the modifications of the minor parts.

physics.data-an↗

arXiv2011

What can we still learn from Brownian motion?

Recent result of the numerical simulation of stochastic motion of conservative mechanical or weakly damped Brownian motion subject to conservative forces reveals that, in the case of Gaussian random forces, the path probability depends exponentially on Lagrangian action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian/Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory, Liouville theorem of conservation of phase distribution breaks down. This opens a way to the Boltzmann H theorem. We argue that the randomness is a crucial distinction between two kingdoms of Hamiltonian/Lagrangian mechanics: the stochastic dynamics and the regular one which is a special case of the first one for vanishing randomness. This distinction was missing in the criticisms of this theorem from Loschmidt, Poincaré and Zermelo.

cond-mat.stat-mech↗

arXiv2010

The uncertainty measure for q-exponential distribution function

Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained here can be considered as a new entropic form for the abnormal physical systems with complex interaction. The entropy obtained here also presents non-additive property for two independent subsystems and it will tend to the Boltzmann-Gibbs entropy when the nonextensive parameter q->1. It is very important to find that for different systems with any q, this entropic form is always concave and the systemic entropy is maximizable.

math-ph↗

arXiv2010

A probabilistic mechanics theory for random dynamics

This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to the Newtonian laws, it is shown that the experimental verification of Newton law in a random motion implies a stochastic extension of the virtual work principle and the least action principle, i.e., =0 and =0 averaged over all the random paths instead of dW=0 and dA=0 for single path in regular dynamics. A probabilistic mechanics is formulated and applied to thermodynamic system. Several known results, rules and principles can be reproduced and justified from this new point of view. To mention some, we have obtain the entropy variation of the free expansion of gas and heat conduction without considering local equilibrium, and a violation of the Liouville theorem and Poincaré recurrence theorem, which allows to relate the entropy production to the work performed by random forces in nonequilibrium process.

cond-mat.stat-mech↗

arXiv2009

A counterexample against the Lesche stability of a generic entropy functional

We provide a counterexample to show that the generic form of entropy S(p)=sum_i g(p_i) is not always stable against small variation of probability distribution (Lesche stability) even if is concave function on [0,1] and analytic on ]0,1]. Our conclusion is that the stability of such a generic functional needs more hypotheses on the property of the function g, or in other words, the stability of entropy cannot be discussed at this formal stage.

cond-mat.stat-mech↗

arXiv2008

A dialectical view of the variational principles of mechanics

The aim of this work is to provide a possible philosophical motivation to the variational principles of physics in general and a possible way to unify the axiomatizations of mechanics theories. The leitmotif of this work is a dialectical view of the world: any smooth motion in nature is the consequence of the interplay and dynamical balance between pairs of opposite elements of the motion. We stress that the opposite property here differs from the common sense of opposing elements (of conflicting appearance but of same nature) such action/reaction forces between two bodies. The opposite elements here are incompatible and mutual exclusive in nature, with contrasting and complementary characteristics such as active/passive, disorder/order, curvature/flatness, etc. The dynamical balance is defined by an invariant variational relationship between all the pairs of opposite elements active in the considered motion. From this idea, an axiomatization of quantum mechanics is proposed in addition to the derivation of several existing variational principles of mechanics.

physics.hist-ph↗

arXiv2008

Possible canonical distributions for finite systems with nonadditive energy

It is shown that a small system in thermodynamic equilibrium with a finite thermostat can have a q-exponential probability distribution which closely depends on the energy nonextensivity and the particle number of the thermostat. The distribution function will reduce to the exponential one at the thermodynamic limit. However, the nonextensivity of the system should not be neglected.

cond-mat.stat-mech↗