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This regime is denoted by OSC in fig. 2. It is easy to check that ̂ T$_{2}$ ( ̂ M ) ⩾ ̂ T$_{1}$ ( ̂ M ) (with equality only for ̂ M = 2( ̂ S + 1)). For all measured ̂ T with ̂ T$_{2}$ ⩾ ̂ T > ̂ T$_{1}$ , denoted by NESS in fig. 2, our new criterion establishes a NESS on the basis of two-state trajectories which do not exhibit oscillatory behaviour. While for ̂ S ≃ 1 the newly established region of NESSs beyond the oscillatory regime is rather small, see fig. 2(b), both for S ≪ 1 and 

for ̂ S ≫ 1 the present analysis shows a large regime of newly ascertained NESSs. In the latter two cases, the oscillatory regime is, for ̂ S ⩽ 0 . 5, totally absent or rather small, see figs. 2(a) and (c), respectively. 

For fixed ̂ S the phase diagrams of physically admissi- ble ( ̂ M, ̂ T ) values are restricted to ̂ M ⩽ 4 ̂ S and ̂ T ⩽ ̂ S $^{2}$, since values outside this range would require negative k$_{ij}$ values. Moreover, for ̂ M ⩽ 2 ̂ S , only T ⩽ T$_{1}$ can be re- 

