The H-theorem for the entropy of waves

Highlights: • The nonequilibrium entropy of classical plasma waves is defined. • The H-theorem for this entropy is derived. • The formulation enables us to define the Helmholtz free energy of waves in plasmas. In a previous study I defined the nonequilibrium entropy of classical waves in terms of the density matrix of the wave amplitude (the square root of the wave action density). In the present work, I derive the H-theorem for this entropy for weak nonlinear waves whose equations of motion are written in a symplectic form. This formulation enables us to define the Helmholtz free energy of waves in classical plasmas.