Entropy of the Dirac field in Schwarzschild-de Sitter space-time via the membrane model

There are two event horizons in Schwarzschild-de Sitter space-time, a black hole horizon and a cosmological horizon. They have different temperatures. The radiation between them is of course not in thermal equilibrium. According to the membrane model suggested by us, the two horizons can be thought of as two independent thermodynamic systems in equilibrium. Their Dirac field entropies are calculated via a membrane model. The result shows that the entropy of the Dirac field is proportional to the sum of the areas of the two event horizons. If we choose the same cutoff as that of Klein-Gordon field, the entropy of the Dirac field is 31/2 times that of Klein-Gordon field. This agrees with previous results.