The principle of detailed balance (DB) states that every kinetic transition in a system with many micro-states, \(\mu \) , is balanced, on average, with the opposite transition, \(\mu _i\leftrightharpoons \mu _j\) . The current perception is that, on the scale of the most elementary degrees of freedom, DB is satisfied only in equilibrium systems, although a rigorous proof exists only for thermal systems. It is believed that, on this scale, non-equilibrium steady states can only be balanced by cycles, such as \(A\rightarrow B\rightarrow C\rightarrow A\) . We report here experiments on a family of out-of-equilibrium quasi-statically cyclically sheared granular systems, which appear to show robust DB. We then analyse in detail the concept and interpretation of DB and show that our systems are the exact equivalent of chemically reactive systems in thermal equilibrium. We therefore conclude that our non-equilibrium systems do indeed satisfy this principle. We further study the approach to DB as a function of system size and time. Given the significant progress to which this principle has led in equilibrium systems, these observations may pave the way for better models of the dynamics and statistical mechanics of these and potentially other non-equilibrium systems.
