Table 1. The detailed analogy between evolutionary dynamics and statistical physics
Object Evolutionary dynamic Statistical physics
State variable  Additive fitness and energy  Population size and temperature νMoran = N – 1 β = 1/kB T  Boltzmann factor  Invariance fi → Cfi Ei → Ei + C
Free fitness and free energy  Equilibrium scale ν(xj – xi ) = 1 β(Ej – Ei ) = 1
• State variable, Additive fitness and energy, Population size and temperature, Boltzmann factor, and Free fitness and free energy are explained in the text. (Invariance) The analogy is also reflected in the symmetries in the representation of physical and evolutionary systems. Namely, because the representation of a physical system is invariant to the addition of a constant to the energy of all the microscopic states, the evolutionary system is invariant to multiplying the fitness in the system by a constant. The invariance takes precisely the same form if we replace fitness by the additive fitness, which is analogous to energy.