# Superpositions of mechanical processes, decomposable coherence and fluctuation relations. (arXiv:1812.08159v2 [quant-ph] UPDATED)

In Newtonian mechanics, any closed-system dynamics of a composite system in a
microstate will leave all its individual subsystems in distinct microstates,
however this fails dramatically in quantum mechanics due to the existence of
quantum entanglement. Here we introduce the notion of a coherent work
process', and show that it is the direct extension of a work process in
classical mechanics into quantum theory. This leads to the notion of
decomposable' and `non-decomposable' quantum coherence and gives a new
perspective on recent results in the theory of asymmetry as well as early
analysis in the theory of classical random variables. Within the context of
recent fluctuation relations, originally framed in terms of quantum channels,
we show that coherent work processes play the same role as their classical
counterparts, and so provide a simple physical primitive for quantum coherence
in such systems. We also introduce a pure state effective potential as a tool
with which to analyze the coherent component of these fluctuation relations,
and which leads to a notion of temperature-dependent mean coherence, provides
connections with multi-partite entanglement, and gives a hierarchy of quantum
corrections to the classical Crooks relation in powers of inverse temperature.