Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator

Mongkolsakulvong, S.; Chaikhan, P.; Frank, T. D.

doi:10.1140/epjb/e2012-20720-4

Cited by 17 publications

(8 citation statements)

References 32 publications

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“…Special mention can be made of the Lotka-Volterra predator-prey systems [29,30] and those of Nambu [31]. Both receive considerable attention [29][30][31][32][33][34][35][36][37]. In the particular case of a Hamiltonian system with degrees of freedom the phase space dimension is N = 2 , and the location x in phase space is given by the complete set of generalized coordinates and the corresponding conjugate momenta, x = ( In the case of a divergenceless dynamical system one has…”

Section: Classical Density Matrixmentioning

confidence: 99%

Classical analogue of the statistical operator

Plastino

Plastino²,

Zander

2014

Open Physics

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Abstract:We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system. PACS

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Section: Classical Density Matrixmentioning

confidence: 99%

Classical analogue of the statistical operator

Plastino

Plastino²,

Zander

2014

Open Physics

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“…In earlier work, a stochastic version of Nambu mechanics has been proposed that is suitable to address both active and purely dissipative systems [7,19,32,33]. These studies focused on the Boltzmann-Gibbs-Shannon thermostatistics.…”

Section: Nambu Dynamics: Stochastic Casementioning

confidence: 99%

Active and Purely Dissipative Nambu Systems in General Thermostatistical Settings Described by Nonlinear Partial Differential Equations Involving Generalized Entropy Measures

Frank

2016

Entropy

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Abstract:In physics, several attempts have been made to apply the concepts and tools of physics to the life sciences. In this context, a thermostatistic framework for active Nambu systems is proposed. The so-called free energy Fokker-Planck equation approach is used to describe stochastic aspects of active Nambu systems. Different thermostatistic settings are considered that are characterized by appropriately-defined entropy measures, such as the Boltzmann-Gibbs-Shannon entropy and the Tsallis entropy. In general, the free energy Fokker-Planck equations associated with these generalized entropy measures correspond to nonlinear partial differential equations. Irrespective of the entropy-related nonlinearities occurring in these nonlinear partial differential equations, it is shown that semi-analytical solutions for the stationary probability densities of the active Nambu systems can be obtained provided that the pumping mechanisms of the active systems assume the so-called canonical-dissipative form and depend explicitly only on Nambu invariants. Applications are presented both for purely-dissipative and for active systems illustrating that the proposed framework includes as a special case stochastic equilibrium systems.

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“…The mathematical model of composed dynamical system with finite spectrum of the energies consists of the following principal elements [14][15][16]. The state of the n-ary composed dynamical system is defined by the n-degree polynomial function f (X ).…”

Section: Applications To Dynamical Systemsmentioning

confidence: 99%

Pascal Matrix Representation of Evolution of Polynomials

Yamaleev

2015

Int. J. Appl. Comput. Math

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Pascal matrix is an adjoint operator of the differential operator of translation. This feature of the Pascal matrix is used in order to construct evolution equations for coefficients of polynomials induced by shifts of the roots. Under certain initial data solutions of the evolution equations are given by sequences of the Appell polynomials. The Pascal matrix is applied to calculate coefficients of the invariant polynomial and to construct a new algorithm of deflation.

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Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator

Cited by 17 publications

References 32 publications

Classical analogue of the statistical operator

Classical analogue of the statistical operator

Active and Purely Dissipative Nambu Systems in General Thermostatistical Settings Described by Nonlinear Partial Differential Equations Involving Generalized Entropy Measures

Pascal Matrix Representation of Evolution of Polynomials

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