Biological behavior in a physical world: Understanding and applying the essential chemical physics of biomolecules Non-equilibrium principles govern cell behavior at molecular scales and beyond. One of the most important examples is the cell’s use of a (non-equilibrium) proton electrochemical gradient to synthesize ATP - a task carried out by the ATP synthase complex using an elaborate rotary mechanism. Because much simpler mechanisms exist to generate ATP from a proton gradient, we attempt to quantify the advantages of the rotary mechanism using a physics-based systems biology approach. On a more microscopic and general level, we can understand key principles of non-equilibrium behavior based on a fairly simple pictorial analysis of trajectories - i.e., on traces of molecular motion over time. These ‘pictorial principles’ lead directly to practical tools for correcting potentially significant bias in Markov analyses of complex systems and to the ‘weighted ensemble’ strategy for orchestrating parallel simulations in a way that can yield key observables using significantly less computing than ordinary parallelization. These principles and strategies are applied to molecular and cell-scale examples.