Characterizing chaos in systems subjected to parameter drift

Jánosi, Dániel; Tél, Tamás

doi:10.1103/physreve.105.l062202

Cited by 5 publications

(3 citation statements)

References 32 publications

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“…We note that, aside from plume diagrams, other methods originating in chaotic dynamics could also be utilized to characterize global climate variables. For example, the recently developed method of EAPD (ensemble-averaged pairwise distance) (Jánosi and Tél, 2022), which monitors the phase space distance between trajectories in an ensemble, seems particularly well suited for problems requiring an ensemble approach. The application of such methods could be the subject of future papers.…”

Section: Discussionmentioning

confidence: 99%

An ensemble based approach for the effect of climate change on the dynamics of extremes

Herein,

Jánosi,

Tél

2023

Front. Earth Sci.

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In view of the growing importance of climate ensemble simulations, we propose an ensemble approach for following the dynamics of extremes in the presence of climate change. A strict analog of extreme events, a concept based on single time series and local observations, cannot be found. To study nevertheless typical properties over an ensemble, in particular if global variables are of interest, a novel, statistical approach is used, based on a zooming in into the ensemble. To this end, additional, small sub-ensembles are generated, small in the sense that the initial separation between the members is very small in the investigated variables. Plume diagrams initiated on the same day of a year are generated from these sub-ensembles. The trajectories within the plume diagram strongly deviate on the time scale of a few weeks. By defining the extreme deviation as the difference between the maximum and minimum values of a quantity in a plume diagram, i.e., in a sub-ensemble, a growth rate for the extreme deviation can be extracted. An average of these taken over the original ensemble (i.e., over all sub-ensembles) characterizes the typical, exponential growth rate of extremes, and the reciprocal of this can be considered the characteristic time of the emergence of extremes. Using a climate model of intermediate complexity, these are found to be on the order of a few days, with some difference between the global mean surface temperature and pressure. Measuring the extreme emergence time in several years along the last century, results for the temperature turn out to be roughly constant, while a pronounced decaying trend is found in the last decades for the pressure.

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Section: Discussionmentioning

confidence: 99%

An ensemble based approach for the effect of climate change on the dynamics of extremes

Herein,

Jánosi,

Tél

2023

Front. Earth Sci.

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“…The alternate program to characterize entropy dynamics via formal ρ dynamics [1-3] arising from interest in the quantum limit, or via an ensemble ρ constructed from individual trajectories [4-8] established a connection between thermodynamic entropy growth and the dynamical loss of information about trajectories. Recent discussions use ensemble dynamics to help understand systems with parameter drift as well as to as snapshot techniques to capture the shape of invariant distributions [9,10]. However, progress is hampered since calculating ρ dynamics, either using many individual trajectories OR by propagating partial differential equations, prove computationally challenging.…”

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confidence: 99%

Permutation entropy of indexed ensembles: quantifying thermalization dynamics

2023

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We introduce ‘PI-Entropy’ Π(ρ ̃) (the Permutation entropy of an Indexed ensemble) to quantify mixing due to complex dynamics for an ensemble ρ of di erent initial states evolving under identical dynamics. We nd that Π(ρ ̃) acts as an excellent proxy for the thermodynamic entropy S(ρ) but is much more computationally e cient. We study 1-D and 2-D iterative maps and nd that Π(ρ ̃) dynamics distinguish a variety of system time scales and track global loss of information as the ensemble relaxes to equilibrium. There is a universal S-shaped relaxation to equilibrium for generally chaotic systems, and this relaxation is characterized by a shu ing timescale that correlates with the system’s Lyapunov exponent. For the Chirikov Standard Map, a system with a mixed phase space where the chaos grows with nonlinear kick strength K, we nd that for high K, Π(ρ ̃) behaves like the uniformly hyperbolic 2-D Cat Map. For low K we see periodic behavior with a relaxation envelope resembling those of the chaotic regime, but with frequencies that depend on the size and location of the initial ensemble in the mixed phase space as well as K. We discuss how Π(ρ ̃) adapts to experimental work and its general utility in quantifying how complex systems change from a low entropy to a high entropy state.

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“…The alternate program to characterize entropy dynamics via formal ρ dynamics [1][2][3] arising from interest in the quantum limit, or via an ensemble ρ constructed from individual trajectories [4][5][6][7][8] established a connection between thermodynamic entropy growth and the dynamical loss of information about trajectories. Recent discussions use ensemble dynamics to help understand systems with parameter drift as well as to as snapshot techniques to capture the shape of invariant distributions [9,10]. However, progress is hampered since calculating ρ dynamics, either using many individual trajectories OR by propagating partial differential equations, prove computationally challenging.…”

mentioning

confidence: 99%

Permutation entropy of indexed ensembles: Quantifying thermalization dynamics

Aragoneses¹,

Kapulkin²,

Pattanayak³

2022

Preprint

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We introduce 'PI-Entropy' Π(ρ) (the Permutation entropy of an Indexed ensemble) to quantify mixing due to complex dynamics for an ensemble ρ of different initial states evolving under identical dynamics. We find that Π(ρ) acts as an excellent proxy for the thermodynamic entropy S(ρ) but is much more computationally efficient. We study 1-D and 2-D iterative maps and find that Π(ρ) dynamics distinguish a variety of system time scales and track global loss of information as the ensemble relaxes to equilibrium. There is a universal S-shaped relaxation to equilibrium for generally chaotic systems, and this relaxation is characterized by a shuffling timescale that correlates with the system's Lyapunov exponent. For the Chirikov Standard Map, a system with a mixed phase space where the chaos grows with nonlinear kick strength K, we find that for high K, Π(ρ) behaves like the uniformly hyperbolic 2-D Cat Map. For low K we see periodic behavior with a relaxation envelope resembling those of the chaotic regime, but with frequencies that depend on the size and location of the initial ensemble in the mixed phase space as well as K. We discuss how Π(ρ) adapts to experimental work and its general utility in quantifying how complex systems change from a low entropy to a high entropy state.

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Characterizing chaos in systems subjected to parameter drift

Cited by 5 publications

References 32 publications

An ensemble based approach for the effect of climate change on the dynamics of extremes

An ensemble based approach for the effect of climate change on the dynamics of extremes

Permutation entropy of indexed ensembles: quantifying thermalization dynamics

Permutation entropy of indexed ensembles: Quantifying thermalization dynamics

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