Energy dissipation from combining incompatible equilibrium systems

Energy dissipation in kinetic systems often arises due to explicit driving from a specific interaction or mechanism that breaks detailed balance. The resulting nonequilibrium steady-state has non-zero probability currents leading to irreversible dissipative cycles in the dynamics. We explore an alternative way to break detailed balance via the combination of multiple equilibrium mechanisms that are not fully compatible. In particular, for both discrete and continuum models, we derive commutation-like relations that can be used to identify whether two equilibrium interactions remain in equilibrium when combined. In cases where detailed balance is broken the entropy production rate is generically peaked as the relative strength of the underlying equilibrium interactions is tuned. Our reinterpretation of nonequilibrium systems as a cross-over between two or more equilibrium systems leads to new analytical tools for analyzing such systems, for example matching perturbation theories around the equilibrium limits. We apply these ideas to the active Ising model and systems of noisy oscillators, in which equilibrium mechanisms such as diffusion, spin alignment, and phase exchange are combined to give rise to nonequilibrium collective behaviors: flocking and synchronization.