We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different critical p
oints arising for different character-dependent grouping mechanisms. These critical points move in opposite directions as the populations diversity decreases. Our analytical theory helps explain why a particular class of universality is so common in the real world, despite fundamental differences in the underlying entities. Furthermore, it correctly predicts the non-monotonic temporal variation in connectivity observed recently in one such system.
Even photosynthesis -- the most basic natural phenomenon underlying Life on Earth -- involves the non-trivial processing of excitations at the pico- and femtosecond scales during light-harvesting. The desire to understand such natural phenomena, as w
ell as interpret the output from ultrafast experimental probes, creates an urgent need for accurate quantitative theories of open quantum systems. However it is unclear how best to generalize the well-established assumptions of an isolated system, particularly under non-equilibrium conditions. Here we compare two popular approaches: a description in terms of a direct product of the states of each individual system (i.e. a local approach) versus the use of new states resulting from diagonalizing the whole Hamiltonian (i.e. a global approach). We show that their equivalence fails when the system is open, in particular under the experimentally ubiquitous condition of a temperature gradient. By solving for the steady-state populations and calculating the heat flux as a test observable, we uncover stark differences between the formulations. This divergence highlights the need to establish rigorous ranges of applicability for such methods in modeling nanoscale transfer phenomena -- including during the light-harvesting process in photosynthesis.
