Exact correspondences between seemingly different concepts play important role in all fields of physics. An example is the fluctuation-dissipation theorem, which states that the linear response of a system to externally applied forces corresponds to the system fluctuations.
In the last decade, the fluctuation-dissipation theorem has initiated important developments in quantum transport, quantum computation, and other similar phenomenological theories. This theorem can be extended to nonlinear responses and to full counting statistics, giving more extended sets of similar relations.
The Shannon entropy in quantum physics is considered unphysical, or non-observable, due to its nonlinear dependence on density matrix. So is the generalized Shannon entropy, called Renyi entropies --named after the French Mathematician and Physicist Alfred Renyi.
An interesting and non-trivial question is:
Is there any relation between the flows of entropy and the physical flows?
The answer to the question, is YES!
A novel relation is presented in the following research article that is similar to the fluctuation-dissipation theorem in spirit and provides an exact correspondence between the flows of quantum entropy and full counting statistics of energy transfers.
By: Mohammad H. Ansari
1- Exact correspondence between Renyi quantum entropy flows and physical flows,
M. H. Ansari and Yu. V. Nazarov,
To appear in Phys. Rev. B., arXiv:1502.08020
2- Renyi entropy flows from quantum heat engines,
M. H. Ansari and Yu. V. Nazarov, Phys. Rev. B 91, 104303 (2015) arxiv:1408.3910