  We demonstrate with an experiment how molecules are a natural test-bed for
probing fundamental quantum thermodynamics. Single-molecule spectroscopy has
undergone transformative change in the past decade with the advent of
techniques permitting individual molecules to be distinguished and probed. By
considering the time-resolved emission spectrum of organic molecules as arising
from quantum jumps between states, we demonstrate that the quantum Jarzynski
equality is satisfied in this set-up. This relates the heat dissipated into the
environment to the free energy difference between the initial and final state.
We demonstrate also how utilizing the quantum Jarzynski equality allows for the
detection of energy shifts within a molecule, beyond the relative shift.
