Thermodynamic relations in a driven lattice gas: numerical exprements

We explore thermodynamic relations in non-equilibrium steady states with numerical experiments on a driven lattice gas. After operationally defining the pressure and chemical potential in the driven lattice gas, we confirm numerically the validity of the integrability condition (the Maxwell relation) for the two quantities whose values differ from those for an equilibrium system. This implies that a free energy function can be constructed for the non-equilibrium steady state that we consider. We also investigate a fluctuation relation associated with this free energy function. Our result suggests that the compressibility can be expressed in terms of density fluctuations even in non-equilibrium steady states.