Fundamental limitations on photoisomerization from thermodynamic resource theories

Small, out-of-equilibrium, and quantum systems defy simple thermodynamic expressions. Such systems are exemplified by molecular switches, which exchange heat with a bath and which can photoisomerize, or change conformation upon absorbing light. The likelihood of photoisomerization depends on kinetic details that couple the molecule's internal energetics with its interaction with the bath, hindering predictions. We derive simple, general bounds on the photoisomerization yield, using a resource-theory model for thermodynamics. The resource-theory framework is a set of mathematical tools, developed in quantum information theory, for modeling any setting in which constraints restrict the operations performable and the systems accessible. Resource theories are being used to generalize thermodynamics to small and quantum settings. Specifically, we use the thermomajorization preorder, a resource-theory generalization of the second law. Thermomajorization follows from the minimal assumptions of energy conservation and a fixed bath temperature. Using thermomajorization, we upper-bound the photoisomerization yield. Then, we compare the bound with expectations from detailed balance and from simple Lindbladian evolution. Our minimal assumptions constrain the yield tightly if a laser barely excites the molecule, such that thermal fluctuations drive conformation changes, and weakly if the laser excites the molecule to one high-energy eigenstate. We also quantify and bound the coherence in the molecule's post-photoisomerization electronic state. Electronic coherence cannot boost the yield in the absence of extra resources, we argue, because modes of coherence transform independently via resource-theory operations. This work illustrates how thermodynamic resource theories can offer insights into complex quantum processes in nature, experiments, and synthetics.