Abstract

The resource theory of quantum thermodynamics has been a very successful theory and has generated much follow up work in the community. It requires energy preserving unitary operations to be implemented over a system, bath, and catalyst as part of its paradigm. So far, such unitary operations have been considered a “free” resource of the theory. However, this is only an idealisation of a necessarily inexact process. Here, we include an additional auxiliary control system which can autonomously implement the unitary by turning “on/off” an interaction. However, the control system will inevitable be degraded by the back-action caused by the implementation of the unitary, which cannot be perfectly implemented. We derive limitations on the quality of the control devise so that the laws of thermodynamics do not change; and prove that the laws of quantum mechanics allow for a sufficiently small back-reaction so that the implementation of thermodynamic resource theoretic operations can be achieved without changing the paradigm, in addition to finding limitations for others.