We show that thermodynamic potentials for an open system can be derived from stationary
probabilities in a stochastic setting based on balance laws and statistical ensembles. Using
a PDE method we find that fundamental thermodynamic relations are derived by taking the
thermodynamic limit of the potentials of the stationary distribution. These results provide
insights into the thermodynamics of open systems as they link stochastic processes,
fluctuation dissipation and mathematical systems theory.