  Small, out-of-equilibrium, and quantum systems defy simple thermodynamic
expressions. Such systems are exemplified by molecular switches, which exchange
heat with a bath. These molecules can photoisomerize, or change conformation,
or switch, upon absorbing light. The photoisomerization probability depends on
kinetic details that couple the molecule's energetics to its dissipation.
Therefore, a simple, general, thermodynamic-style bound on the
photoisomerization probability seems out of reach. We derive such a bound using
a resource theory. The resource-theory framework is a set of mathematical
tools, developed in quantum information theory, used to generalize
thermodynamics to small and quantum settings. From this toolkit has been
derived a generalization of the second law, the thermomajorization preorder. We
use thermomajorization to upper-bound the photoisomerization probability. Then,
we compare the bound with an equilibrium prediction and with a Lindbladian
model. We identify a realistic parameter regime in which the Lindbladian
evolution saturates the thermomajorization bound. We also quantify the energy
coherence in the electronic degree of freedom, and we argue that this coherence
cannot promote photoisomerization. This work illustrates how
quantum-information-theoretic thermodynamics can elucidate complex quantum
processes in nature, experiments, and synthetics.
