Modified Lorenz-Malkus water wheel model: dry friction versus chaos

Karpov, E. A.; Семенов, Михаил Е.; Meleshenko, Peter A.; Klinskikh, A. F.; Pervezentcev, R. E.; Glazkova, M. Yu

doi:10.1088/1742-6596/1368/4/042044

Cited by 2 publications

(1 citation statement)

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“…In the present work we use a mathematical model representing a real thermodynamic machine called the Malkus-Lorenz wheel [25,26,27,28] to study its efficiency and rate of entropy generation as it is driven away from equilibrium. The driving is achieved by affecting the intake and release of matter from and to the environment.…”

Section: Introductionmentioning

confidence: 99%

The thermodynamic efficiency of the Lorenz system

López¹,

Benito²,

Sabuco³

et al. 2022

Preprint

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We study the thermodynamic efficiency of the Malkus-Lorenz waterwheel. For this purpose, we derive an exact analytical formula that describes the efficiency of this dissipative structure as a function of the phase space variables and the constant parameters of the dynamical system. We show that, generally, as the machine is progressively driven far from thermodynamic equilibrium by increasing its uptake of matter from the environment, it also tends to increase its efficiency. However, sudden drops in the efficiency are found at critical bifurcation points leading to chaotic dynamics. We relate these discontinuous crises in the efficiency to a reduction of the attractor's average value projected along the phase space dimensions that contribute to the rate of entropy generation in the system. In this manner, we provide a thermodynamic criterion that, presumably, governs the evolution of far-from-equilibrium dissipative systems towards their self-assembly and synchronization into increasingly complex networks and structures.

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Section: Introductionmentioning

confidence: 99%