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Figure 2
Schematic description of obtaining dynamics in a non-equilibrium system through the ACS (left panel) and CCS (right panel) in the (t, Δt) plane [t′ = t′(t, Δt), t′′ = t′′(t, Δt)]. The time dependency is illustrated by different colors, gradually changing from red to deep blue. For ACS: t′ = t − Δt/2 and t′′ = t + Δt/2. Therefore, at any time moment t0, tcen = (t′ + t′′)/2 = t0 and, thus, the calculated τ can be approximated by the effective dynamics with τ(t0) (see examples for t01 and t02). For CCS: t′ = t and t′′ = t + Δt. Therefore, at any time moment t0, tcen = (t′ + t′′)/2 = t0 + Δt/2. Thus, the relaxation time τ = τ(t0 + Δt/2) cannot be approximated by effective dynamics anymore, except when the system is in quasi-equilibrium and τ(t0 + Δt/2) ≈ τ(t0).

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