通过振荡模式分解线性朗之万系统的热力学耗散及其在神经动力学中的应用
Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics
AI总结：
本研究提出线性朗之万系统熵产生率的振荡模式分解方法，可量化各模式及系统元素的持家熵产生贡献，应用于猴子ECoG数据揭示了清醒与麻醉状态下神经振荡的热力学差异。
摘要：
随机热力学的最新进展阐明了非平衡动力系统中熵产生率（热力学耗散）与信息处理物理极限之间的多种关系。这些发现为分析真实生物系统开辟了新视角。在神经科学领域，量化熵产生的重要性因理解大脑信息处理的需求而受到关注。然而，熵产生率与许多生物系统中常见的振荡之间的关系仍不明确。例如，delta波、theta波和alpha波等神经振荡在大脑信息处理中发挥着关键作用。\n本文推导了线性朗之万系统熵产生率的一种新型分解方式。我们证明，熵产生率的一个组成部分——即持家熵产生率——可分解为来自各振荡模式的独立正贡献。通过这种分解，我们能够计算各振荡模式对持家熵产生率的贡献。此外，当噪声矩阵为对角矩阵时，每个振荡模式的贡献可进一步分解为各系统元素的贡献。\n为验证该分解方法的实用性，我们将其应用于猴子清醒和麻醉状态下记录的皮层脑电图（ECoG）数据集，这两种状态下的振荡特性会发生显著变化。我们在不同猴子身上观察到一致的趋势：麻醉状态下delta频段的贡献大于清醒状态，而theta频段等更高频段的贡献则更小。这些结果使我们能够从随机热力学和信息处理物理极限的角度解释神经振荡的变化。
英文摘要：
Recent developments in stochastic thermodynamics have elucidated various relations between the entropy production rate (thermodynamic dissipation) and the physical limits of information processing in nonequilibrium dynamical systems. These findings have opened new perspectives in analyzing real biological systems. In neuroscience, the importance of quantifying entropy production has attracted attention for understanding information processing in the brain. However, the relationship between the entropy production rate and oscillations, which are common in many biological systems, remains unclear. For instance, neural oscillations like delta, theta, and alpha waves play crucial roles in brain information processing. Here, we derive a novel decomposition of the entropy production rate of linear Langevin systems. We show that one component of the entropy production rate, called the housekeeping entropy production rate, can be decomposed into independent positive contributions from oscillatory modes. Our decomposition enables us to calculate the contribution of oscillatory modes to the housekeeping entropy production rate. In addition, when the noise matrix is diagonal, the contribution of each oscillatory mode can be further decomposed into the contribution of each system element. To demonstrate the utility of our decomposition, we applied it to an electrocorticography (ECoG) dataset recorded during awake and anesthetized conditions in monkeys, where the oscillatory properties change drastically. We showed consistent trends across different monkeys: the contribution of delta band was larger in the anesthetized condition than in the awake condition, while those from higher frequency bands, such as the theta band, were smaller. These results allow us to interpret the changes in neural oscillation in terms of stochastic thermodynamics and the physical limits of information processing.
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