The concept of magnetic entropy, the entropy pertaining to a magnetic configuration, is introduced and illustrated through its application to the description of the magnetic states assumed preferentially by a tokamak and of the transition between them. The magnetic equilibria associated with stationary magnetic entropy admit a bifurcation, and a new state can arise that can be attained spontaneously with an increase in the magnetic entropy. The thermodynamic relations between entropy production, heat transport and plasma energy allow one to express quantitatively the modifications of these quantities generated by the magnetic transition to the new state and to identify it with the L–H transition. The power and temperature thresholds of the transition are expressed in terms of the confinement time of the L state, and definite scalings are derived that compare favourably with observations. The theory implies the hysteresis and the upper density limit of the H state.