Thermodynamics of driven systems with explicitly broken detailed balance

In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose a challenge for a consistent thermodynamic interpretation. Even steady-state potentials like entropy or free energy are no longer state variables. Here, we develop a thermodynamic framework for sample-space-reducing (SSR) processes, as an example of driven systems that explicitly violate detailed balance. By adapting Boltzmann's entropy formula to account for the constrained transition structure of SSR dynamics, we establish thermodynamic relations for these processes. We demonstrate that, despite explicitly broken detailed balance, it remains feasible to define and unambiguously interpret the effective thermodynamic potentials.