We understood how to measure it

A novel correspondence between entropy flow and  statistics of energy exchange was reported in this paper. This is an extension of earlier result by Levitov and Klich on how to measure entropy in systems with charge transfers.

There seems to be an exact correspondence
between Renyi entropy flow
and statistics of energy exchange. 

The situation is fairly similar to the fluctuation-dissipation theorem however the new correspondence links between the Renyi (and Shannon) entropy and physical and measurable quantities.

What is Renyi entropy?

It was proposed by Alfred Renyi in '60s as novel information measures. Shannon entropy is determined from them as an example.

Why measuring entropy? 

Information content in Renyi entropy is a key concept to establish fundamental laws of thermodynamics in small scales. It helps to understand  how to communicate information with quantum devices.

Now between two systems A and B that exchange energy, we understood how to measure the Renyi entropies.

This correspondence can serve as a fundamental approach to study a second law of thermodynamics in quantum scales (if there is any.)