Developments in Nambu mechanics

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

“…The diffusion term, i.e., the third expression on the right-hand side of the equal sign in Equation (11), is nonlinear with respect to P. This type of nonlinear diffusion coefficient has been introduced by Plastino and Plastino in the context of Fokker-Planck equations associated with the non-extensive Tsallis entropy [45] and is a benchmark nonlinearity of nonlinear diffusion equations in material physics [46][47][48]. Due to the fact that in general, the model (9) is nonlinear with respect to P (e.g., see Equation (11)) and in view of the fact that the structure of the model (9) is similar to a Fokker-Planck equation, it has been suggested to refer to Equation (9) as the nonlinear Fokker-Planck equation.…”

“…A variety of oscillatory systems [8][9][10][11][12][13][14] have been studied within the framework of Nambu mechanics. Particles moving on curved surfaces correspond under appropriate conditions to system that live in n-dimensional spaces and satisfy n − 1 invariants, such that Nambu mechanics applies [15][16][17][18][19].…”

“…In electrodynamics, Nambu mechanics has found several applications [5,11,12,20,21]. In particular, the motion of a charged particle in a constant magnetic field can be studied from the perspective of Nambu mechanics [22].…”

Landauer’s Principle and Divergenceless Dynamical Systems

“…Indeed, these two fundamental features allow for deriving many aspects of the canonical statistical mechanical formalism without recourse to the detailed structure of standard Hamiltonian dynamics [24,25]. Among others, the Lotka-Volterra predator-prey systems [26,27] and the Nambu systems [28][29][30][31][32][33] share the vanishing divergence property and admit an integral of motion. If the system A is to behave as a proper "information storage device", it is reasonable to assume that before and after the information erasure process, the systems A and B are only weakly coupled.…”

Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator

“…[7][8][9][10]. Certain electrodynamic [5,[11][12][13][14][15] and biochemical [16,17] problems have been re-formulated using the multi-Hamiltonian approach of Nambu mechanics. Multi-Hamiltonian oscillators generalizing the harmonic oscillator [18,19], chiral models [8] and the Calogero-Moser system [20,21] have been studied in the context of Nambu mechanics.…”