The number of microstates Ω that a closed system can occupy is proportional to its phase space volume: Ω Ω ( U ) = 1 h 0 F ∫ ∫ 1 δ δ U ( H ( x ) − − U ) ∏ ∏ i = 1 F d q i d p i where 1 δ δ U ( H ( x ) − − U ) is an Indicator function. It is 1 if the Hamilton function H (x) at the point x = (q, p) in phase space is between U and U + δU and 0 if not. The constant 1 / h 0 F makes Ω(U) dimensionless. For an ideal gas is Ω Ω ( U ) ∝ ∝ F U F 2 − − 1 δ δ U .