A meaningful expansion around detailed balance

We consider Markovian dynamics modelling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. Asystematic expansion is obtained of the stationary distribution around an equilibrium reference, in orders of the nonequilibrium forcing. The first-order around equilibrium has been known since the work of McLennan (1959 Phys. Rev. 115 1405-9), and involves the transient irreversible entropy flux. The expansion generalizes the McLennan formula to higher orders, complementing the entropy flux with the dynamical activity. The latter is more kinetic than thermodynamic and is a possible realization of Landauer's insight (1975 Phys. Rev. A 12 6368) that, for nonequilibrium, the relative occupation of states also depends on the noise along possible escape routes. In that way, nonlinear response around equilibrium can be meaningfully discussed in terms of two main quantities only, the entropy flux and the dynamical activity. The expansion makes mathematical sense as shown in the simplest cases from exponential ergodicity.