Fluctuation Theorem for Hidden Entropy Production

TL;DR

This paper introduces a fluctuation theorem for hidden entropy production in Markovian models, revealing how entropy changes during variable elimination and providing insights into coarse graining effects.

Contribution

It presents a new integral fluctuation theorem for hidden entropy production applicable to time-reversal invariant variables in Markovian systems.

Findings

Hidden entropy production obeys a new fluctuation theorem.

Entropy production decreases under coarse graining when conditions are met.

In some cases, entropy production can increase after reduction, as shown by the extended multibaker map.

Abstract

In the general process of eliminating dynamic variables in Markovian models, there exists a difference in the irreversible entropy production between the original and reduced dynamics. We call this difference the hidden entropy production, since it is an invisible quantity when only the reduced system's view is provided. We show that this hidden entropy production obeys a new integral fluctuation theorem for the generic case where all variables are time-reversal invariant, therefore supporting the intuition that entropy production should decrease by coarse graining. It is found, however, that in cases where the condition for our theorem does not hold, entropy production may also increase due to the reduction. The extended multibaker map is investigated as an example for this case.