publications

2023

1. 

   A System-Independent Derivation of Preferential Attachment from the Principle of Least Effort

   François Xavier Machu, Ru Julie Wang, Jean Louis Cheng, Jeremy Cocks, and Qiuping Alexandre Wang

   Entropy, 2023

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   Preferential attachment (PA) is a widely observed behavior in many living systems and has been used in modeling many networks. The aim of this work is to show that the mechanism of PA is a consequence of the fundamental principle of least effort. We derive PA directly from this principle in maximizing an efficiency function. This approach not only allows a better understanding of the different PA mechanisms already reported but also naturally extends these mechanisms with a non-power law probability of attachment. The possibility of using the efficiency function as a general measure of attachment efficiency is also investigated.

2021

1. Adv. Complex Syst.

   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

   A. EL KAABOUCHI, F. X. MACHU, J. COCKS, R. WANG, Y. Y. ZHU, and Q. A. WANG

   Advances in Complex Systems, 2021

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   The principle of least effort (PLE) 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 PLE. This 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 nonnegative continuous entropy.

2018

1. J.Phys.Conf.Ser.

   A true least action principle for damped motion

   Qiuping A. Wang, and Ru Wang

   Journal of Physics: Conference Series, Nov 2018

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   This work is a formulation of the least action principle for classical mechanical dissipative systems. We consider a whole conservative system composed of a damped moving body and its environment receiving the dissipated energy. This composite system has a conservative Hamiltonian H = K1 + V1 + H2 where K1 is the kinetic energy of the moving body, V1 its potential energy and H2 the energy of the environment. The Lagrangian is found to be L = K1 − V1 − Ed where Ed is the energy dissipated from the moving body into the environment. The usual variation calculus of least action leads to the correct equation of the damped motion.

2013

1. 

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

   T.L. Lin, R. Wang, W.P. Bi, A. El Kaabouchi, C. Pujos, F. Calvayrac, and Q.A. Wang

   Chaos, Solitons & Fractals, Nov 2013

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   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, divided 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.

2012

1. Eur.Phys.J.B

   About a nonadditivity of energy and entropy

   R. Wang, C. J. Ou, J. C. Chen, and Q. A. Wang

   Nov 2013

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   The mathematical expression of nonadditivity X(1 ∪ 2) = X(1) + X(2) + αX(1)X(2) has been frequently used for the development of statistical physics for nonadditive system, where X is entropy or energy, and α is hoped to be a parameter characterising the nonadditive property of the composite system (1 ∪ 2). Here we show that this relationship cannot hold exactly. In general, α in this expression inevitably depends on how a given system with constant X(1 ∪ 2) is divided into subsystems 1 and 2. Hence mathematical problems may arise when it is used to characterise the nonadditivity of the system. Nevertheless, under some conditions, it is possible to use it as a good approximation.

2. 

   An equilibrium thermostatistics of a nonextensive finite system: Canonical distribution and entropy

   J. Jiang, R. Wang, Y. Lysogorskii, D. Zvezdov, D. Tayurskii, and Q.A. Wang

   Physica A: Statistical Mechanics and its Applications, Nov 2012

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   A simple model is presented to illustrate the equilibrium thermostatistics of a nonentensive finite system. Interaction between the finite system and the reservoir is taken into account as a nonextensive term λH1H2 in the expression of total energy (H1 and H2 are the energy of the finite system and the reservoir respectively, λ is nonadditivity parameter). In the present paper, a case with harmonic reservoir potential is considered. Energy probability distribution, average energy, heat capacity and entropy function for energy distribution are derived in different finite systems including those with constant density of state in energy, the ideal gas and the phonon gas.