Quantum thermodynamics seeks to extend the laws of thermodynamics to equilibrium and non-equilibrium systems on the nano-scale. Over the last decade a large body of theoretical research into quantum thermodynamics has been produced; however, experimental research is yet to catch up with the impressive lead set by theory. This is especially true of quantum information theoretic approaches which have proven an effective means of incorporating quantum effects into thermodynamics but seem resistant to experimental implementation. This thesis aims to counter this shortcoming by proposing concrete physical realisations} of quantum thermodynamics to help bridge the gap between theory and experiment.

This task is approached directly in chapter 2 by constructing an experimental implementation of a fluctuation relation developed from a quantum information theoretic perspective. Our proposal involves the autonomous evolution of a trapped ion and uses a tapered laser beam to implement a position dependent AC Stark shift. In order to test the fluctuation relation we convert the abstract framework of an autonomous quantum Crooks equality into quantum Crooks equalities for coherent, squeezed and cat states. These new relations highlight the physical origins and implications of coherence induced corrections to classical fluctuation relations and prompt a discussion on the interplay between coherence and irreversibility.

In chapter 3 we turn our attention to Gibbs' iconic thought experiments on the work that can be extracted from the mixing of gases. Here we argue that optomechanical setups, involving a cavity in which a membrane is inserted, provide a suitable platform both to generalise such thought experiments to the quantum regime and to explore quantum thermodynamic signatures of distinguishability. We find, in contrast to classical thermodynamics, that the work that can be extracted from the mixing of the two photon gases varies continuously with their distinguishability. Finally, we demonstrate that the bunching of photons, arising from their Bosonic character, generates an energetic footprint that does not exist in classical thermodynamics.