Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics

Abstract

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.