Decomposable Coherence and Quantum Fluctuation Theorems*

How can one define work on a quantum system without requiring the existence of a classical agent manipulating macroscopic equipment? To answer this question, we formulate the problem as can be done in Newtonian mechanics - by introducing a `weight system' with strict global energy conservation. By allowing a system in an arbitrary pure quantum state to interact with a weight system prepared in a well defined state, we are able to study the structure of `coherent energy transfers'. We then define a coherent work process and show that this is related to the notion of decomposability of a classical random variable. Maintaining the nomenclature, we introduce the notion of decomposable coherence. Furthermore, we show that coherent work processes can only map coherent states to coherent states, and they become classical work processes in a conservative potential as h goes to 0.

We then relate this framework to recent work in the study of quantum fluctuation theorems [1,2]. We find an induced definition of coherent work consistent with the previous framework. Furthermore, we show that entanglement generation is exponentially more probable than de-correlating dynamics.


[1] Johan Åberg Phys. Rev. X 8, 011019
[2] Z. Holmes et al arXiv:1806.11256