Lyapunov spectra and fluctuation relations: Insights from the Galerkin-truncated Burgers equation

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This analysis explores the relationship between fluctuation relations and negative viscosity in the Burgers equation, highlighting chaotic dynamics.

Lyapunov spectra indicate chaotic dynamics, revealing that attractors span the entire phase space of the Burgers equation.
Negative viscosity events occur solely within the thermalized regime of the time-reversible Burgers equation.
Fluctuation relations such as the Gallavotti–Cohen relation are satisfied by negative viscosity events, affecting statistical properties.
Local Lyapunov spectra were calculated, emphasizing the connection between energy injection and chaotic behavior in the system.

Das et al. (2025) studied this question.

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This analysis explores the relationship between fluctuation relations and negative viscosity in the Burgers equation, highlighting chaotic dynamics.