0 0.1 0.2 0.3 -2 0 2 4 s * s * r s * id s * im s * ex FIG. 8: s$_{id}$ ∗ , s ∗ $_{r}$, s ∗ im and s ∗ ex versus density for T ∗ = 0 . 2. diffusivity anomalies. The non-monotonic behaviour of s ∗ ex in the anomalous regime seems to be reflected only in s ∗ $_{im}$. The strong resemblance between s ∗ id and s ∗ r in T - and ρ -dependence suggests that this term reflects the generic effects of thermal fluctuations and spatial con- finement on the entropy but in general it is insensitive to the structural details associated with the interplay between the two length scales in the anomalous regime. Fig. 9 compares, for various isotherms, the density dependence of three different entropy estimators: (a) s ∗ $_{im}$, the imaginary mode contribution to the entropy, (in the graph, form the value of s ∗ im it is subtracted 2), (b) s ∗ $_{2}$, the pair correlation entropy, and (c) s ∗ ω $_{E}$, the entropy estimated using the Einstein model for the liquid, Eq. (13). As discussed in Section IV.A, the s ∗ 2 behaviour is very similar in density and temperature dependence to s ∗ $_{ex}$, indicating that the pair correlation contribution to the entropy is sufficient to capture the essential features of the anomalies. s ∗ ω $_{E}$, derived from the Einstein model, is very similar to s ∗ $_{r}$, presumably because of the use of the harmonic oscillator representation of the entropy. The non-monotonic behaviour of ω$_{E}$ ( ρ ) results in small plateau at low temperatures. The overall decrease in S$_{ω}$$_{E}$ with density is much too steep and monotonic compared with s ∗ ex and s ∗ $_{2}$. In contrast, s ∗ im = s ∗ − s ∗ $_{r}$, captures the behaviour of the entropy within the anomalous region very successfully. The relative displacement of s ∗ $_{im}$( ρ ) curves for different isotherms is very small, consistent with the earlier observation that the overall effect of thermal and 15