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Entropy 2017, 19(7), 302; doi:10.3390/e19070302

Large Scale Emerging Properties from Non Hamiltonian Complex Systems

Istituto di Scienze Marine (ISMAR-CNR), Forte Santa Teresa, 19032 La Spezia, Italy
Received: 31 May 2017 / Revised: 22 June 2017 / Accepted: 23 June 2017 / Published: 26 June 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
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Abstract

The concept of “large scale” depends obviously on the phenomenon we are interested in. For example, in the field of foundation of Thermodynamics from microscopic dynamics, the spatial and time large scales are order of fraction of millimetres and microseconds, respectively, or lesser, and are defined in relation to the spatial and time scales of the microscopic systems. In large scale oceanography or global climate dynamics problems the time scales of interest are order of thousands of kilometres, for space, and many years for time, and are compared to the local and daily/monthly times scales of atmosphere and ocean dynamics. In all the cases a Zwanzig projection approach is, at least in principle, an effective tool to obtain class of universal smooth “large scale” dynamics for few degrees of freedom of interest, starting from the complex dynamics of the whole (usually many degrees of freedom) system. The projection approach leads to a very complex calculus with differential operators, that is drastically simplified when the basic dynamics of the system of interest is Hamiltonian, as it happens in Foundation of Thermodynamics problems. However, in geophysical Fluid Dynamics, Biology, and in most of the physical problems the building block fundamental equations of motions have a non Hamiltonian structure. Thus, to continue to apply the useful projection approach also in these cases, we exploit the generalization of the Hamiltonian formalism given by the Lie algebra of dissipative differential operators. In this way, we are able to analytically deal with the series of the differential operators stemming from the projection approach applied to these general cases. Then we shall apply this formalism to obtain some relevant results concerning the statistical properties of the El Niño Southern Oscillation (ENSO). View Full-Text
Keywords: Non Hamiltonian complex systems; Fokker Planck Equation; transport coefficients; El Niño-La Niña; Lie evolution; projection approach Non Hamiltonian complex systems; Fokker Planck Equation; transport coefficients; El Niño-La Niña; Lie evolution; projection approach
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bianucci, M. Large Scale Emerging Properties from Non Hamiltonian Complex Systems. Entropy 2017, 19, 302.

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