I have been measuring my heart rate recovery after exercise and I see that it can be fit reasonably well using a single exponential:
$HeartRate(t) = HR_{max} \times e^{-t/\tau} + HR_{resting}$
This observation is further supported by this paper: https://pubmed.ncbi.nlm.nih.gov/24494748/
From Wikipedia: "A quantity is subject to exponential decay if it decreases at a rate proportional to its current value"
So, the exponential decay suggests that the ability to slow down the heart depends on the heart rate itself. A faster beating heart somehow produces more of the signal to slow down the heart.
Is this the case? What is the mechanism that allows for such a feedback loop of the heart rate? Is the signal sent through the nerves as the heart muscles contract, or is the blood flow that allows a signal to travel?
Is there another way to explain the mono-exponential decay?
Here is an example from yesterday's run. I sprinted and then walked very slowly a few times. My heart recovery lifetime ($\tau$) including only the first three decays is 53 +/- 4 seconds. The last decay is after I ran up the stairs and then sat down, and its lifetime is of only 22 seconds.