Not All Fluctuations Are Created Equal: Spontaneous Variations in Thermodynamic Function

We identify macroscopic functioning arising during a thermodynamic system's typical and atypical behaviors, thereby describing system operations over the entire set of fluctuations. We show how to use the information processing second law to determine functionality for atypical realizations and how to calculate the probability of distinct modalities occurring via the large-deviation rate function, extended to include highly correlated, memoryful environments and systems. Altogether, the results complete a theory of functional fluctuations for complex thermodynamic nanoscale systems operating over finite periods. In addition to constructing the distribution of functional modalities, one immediate consequence is a cautionary lesson: ascribing a single, unique functional modality to a thermodynamic system, especially one on the nanoscale, can be misleading, likely masking an array of simultaneous, parallel thermodynamic transformations that together may also be functional. In this way, functional fluctuation theory alters how we conceive of the operation of biological cellular processes, the goals of engineering design, and the robustness of evolutionary adaptation.