Bound on efficiency of heat engine from uncertainty relation viewpoint

Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. As for example, heat engine can be modeled with an infinite potential well as working substance to determine the efficiency and work done. However, in this method, the relation between quantum observables and the physically measurable parameters i.e. the efficiency and work done is not well understood from the quantum mechanics approach. A detailed analysis is needed to link thermodynamical variables (on which efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of sum uncertainty relation of position and momentum operator with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through uncertainty relation.