We describe the existence of an entropy for lattice gas systems of Fermi–Dirac type based on a generalized semi-detailed balance condition. We demonstrate some essential equilibrium and non-equilibrium fluctuation and dissipation properties, including the so-called Onsager's reciprocity relations, as a consequence of this condition. Requirements for the existence of certain statistical properties in discrete lattice gas systems are not directly inferred from those in real continuous systems, but are closely related. Hence understanding in detail the causes and results for lattice gas systems may provide further insights into fundamental microscopic physical processes.