2026-06-22 東京大学
熱力学的散逸の振動モード分解
＜関連情報＞
- https://www.c.u-tokyo.ac.jp/info/news/topics/20260622140000.html
- https://www.pnas.org/doi/abs/10.1073/pnas.2530617123
非線形ランジュバン動力学における熱力学的散逸のクープマンモード分解 Koopman mode decomposition of thermodynamic dissipation in nonlinear Langevin dynamics
Daiki Sekizawa, Sosuke Ito, and Masafumi Oizumi
Proceedings of the National Academy of Sciences Published: June 18, 2026
DOI:https://doi.org/10.1073/pnas.2530617123
Significance
Oscillations in nonlinear systems underlie phenomena from chemical waves to neural rhythms. Such oscillations in noisy environments incur thermodynamic dissipation, yet how their frequency, amplitude, and coherence shape this cost remains unclear. Here, using Koopman mode decomposition, which recasts nonlinear dynamics as linear evolution in function space, we show that this cost, measured by the housekeeping entropy production rate, splits into contributions from oscillatory modes, each scaling as the squared frequency times its intensity. The decomposition also implies that, at fixed cost, faster modes face tighter amplitude limits. The framework reveals frequency-resolved structure invisible in the total cost, showing that dissipation can arise from one dominant mode or a broad spectrum in nonlinear phenomena such as bifurcation and coherent resonance.
Abstract
Nonlinear oscillations are commonly observed in complex systems far from equilibrium, such as living organisms. These oscillations are essential for sustaining vital processes, like neuronal firing, circadian rhythms, and heartbeats. In such systems, thermodynamic dissipation is necessary to maintain oscillations against noise. However, due to their nonlinear dynamics, it has been challenging to determine how the characteristics of oscillations, such as frequency, amplitude, and coherent patterns across elements, influence dissipation. To resolve this issue, we employ Koopman mode decomposition, which recasts nonlinear dynamics as a linear evolution in a function space. This linearization allows the dynamics to be decomposed into temporal oscillatory modes coherent across elements, with the Koopman eigenvalues determining their frequencies. Using this method, we decompose thermodynamic dissipation caused by nonconservative forces into contributions from oscillatory modes in overdamped nonlinear Langevin dynamics. We show that the dissipation from each mode is proportional to its frequency squared and its intensity, providing an interpretable, mode-by-mode picture. In the noisy FitzHugh–Nagumo model, we demonstrate the effectiveness of this framework in quantifying the impact of oscillatory modes on dissipation during nonlinear phenomena like coherent resonance and bifurcation. For instance, our analysis of coherent resonance reveals that the greatest dissipation at the optimal noise intensity is supported by a broad spectrum of frequencies, whereas at nonoptimal noise levels, dissipation is dominated by specific frequency modes. Our work offers a general approach to connecting oscillations to dissipation in noisy environments and improves our understanding of diverse oscillation phenomena from a nonequilibrium thermodynamic perspective.
