  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.
