Soliton-breather approach to classical sine-Gordon thermodynamics

Thermodynamics of the Boltzmann gas consisting of solitons, antisolitons, and breathers of the classical sine-Gordon system is studied by taking their interactions into account. A compact expression for the thermodynamic potential is obtained, which agrees with that obtained from the classical limit of the Bethe-ansatz formulation of the quantum sine-Gordon thermodynamics. We further find that the average number of breathers excited at low temperatures (mTM, where m and M are the phonon and the soliton masses, respectively) is half the total number of degrees of freedom of the system.