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 been actively utilized and have opened new perspectives in the analysis of real biological systems. In neuroscience also, the importance of quantifying entropy production has attracted increasing attention as a means to understand the properties of information processing in the brain. However, the relationship between entropy production rate and oscillations, which is prevalent in many biological systems, is unclear. For example, neural oscillations, such as 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 of the components 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 of the Langevin equation is diagonal, the contribution of each oscillatory mode is further decomposed into the contribution of each element of the system. To demonstrate the utility of our decomposition, we apply our decomposition to an electrocorticography dataset recorded during awake and anesthetized conditions in monkeys, wherein the properties of oscillations change drastically. We show the consistent trends across different monkeys; i.e., the contribution of oscillatory modes from the delta band are larger in the anesthetized condition than in the awake condition, while those from the higher-frequency bands, such as the theta band, are smaller. These results allow us to interpret the change in neural oscillation in terms of stochastic thermodynamics and the physical limit of information processing.

中文翻译：

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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


随机热力学的最新发展阐明了非平衡动力学系统中熵产生速率（热力学耗散）和信息处理的物理极限之间的各种关系。这些发现得到了积极利用，并为分析真实生物系统开辟了新的视角。在神经科学中，量化熵产生的重要性也作为了解大脑信息处理特性的一种手段而受到越来越多的关注。然而，熵产生速率与许多生物系统中普遍存在的振荡之间的关系尚不清楚。例如，神经振荡，如 delta、theta 和 alpha 波，在大脑信息处理中起着至关重要的作用。在这里，我们推导出了线性朗之万系统的熵产生率的新分解。我们表明，熵产生率的一个组成部分，称为看家熵产生率，可以分解为来自振荡模式的独立正贡献。我们的分解使我们能够计算振荡模式对管家熵产生率的贡献。此外，当 Langevin 方程的噪声矩阵为对角线时，每个振荡模式的贡献进一步分解为系统每个元素的贡献。为了证明我们分解的效用，我们将分解应用于在猴子清醒和麻醉条件下记录的皮层电图数据集，其中振荡的特性发生了巨大变化。我们展示了不同猴子的一致趋势;即，在麻醉条件下，来自 delta 波段的振荡模式的贡献大于在清醒条件下的贡献，而来自较高频段（例如 theta 波段）的振荡模式的贡献较小。这些结果使我们能够从随机热力学和信息处理的物理极限来解释神经振荡的变化。