  We prove a linear stability-dissipation relation (SDR) for $q$-state Potts
models driven far from equilibrium by a nonconservative force. At a critical
coupling strength, these models exhibit a synchronisation transition from a
decoherent into a synchronised state. In the vicinity of this transition, the
SDR connects the entropy production rate per oscillator to the phase-space
contraction rate, a measure of stability, in a simple way. For large but finite
systems, the SDR implies a minimum-dissipation principle for driven Potts
models as the dynamics selects stable non-equilibrium states with least
dissipation. This principle holds arbitrarily far from equilibrium, for any
stochastic dynamics, and for all $q$.
