Pressure or temperature anisotropy is an intrinsic characteristic of space plasmas, as is often indicated by satellite observation. A set of double-polytropic laws, d(p⊥n−1B1−γ⊥)/dt=0, d(p∥n−γ∥Bγ∥−1)/dt=0, has been proposed and shown to provide a viable closure to the earth’s magnetosheath plasmas. These equations in the limit of γ⊥=2, γ∥=3 and γ⊥=1, γ∥=1 describe the double-adiabatic and double-isothermal states, respectively. This paper gives an overview of the energy equations in gyrotropic plasmas and shows that the double-polytropic laws may be put into conservative forms conveniently implemented for numerical simulation and shock study. In addition, for ultrarelativistic gyrotropic plasmas, the energy equations may also be expressed in terms of the double-polytropic laws. In particular, a relationship of γu=(f+1)/f between the ratio of specific heats, γ, of ultrarelativistic plasmas and the degree of freedom of particles, f, may be established. As a result, for monatomic gas, γu,⊥=1.5 and γu,∥=2, in contrast to γ⊥=2, γ∥=3 for nonrelativistic case, for perpendicular and parallel motions with respect to the magnetic field.