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arXiv · 2406.19499

Strict Lyapunov functions and energy decay in Hamiltonian chains with degenerate damping

Andrey Dymov·Lev Lokutsievskiy·Andrey Sarychev
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Abstract

We consider a Hamiltonian chain of rotators (in general nonlinear) in which the first rotator is damped. Being motivated by problems of nonequilibrium statistical mechanics of crystals, we construct a strict Lyapunov function that allows us to find a lower bound for the total energy dissipation rate when the energy and time are large. Our construction is explicit and its analysis is rather straightforward. We rely on a method going back to Matrosov, Malisoff and Mazenc, which we review in our paper. The method is rather universal and we show that it is applicable to a chain of oscillators as well.

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Andrey Dymov, Lev Lokutsievskiy, Andrey Sarychev. 2024-06-27. Strict Lyapunov functions and energy decay in Hamiltonian chains with degenerate damping. https://arxiv.org/abs/2406.19499

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