A systematic modification of the entropy trajectory ( $$S_\mathrm{m}(T)$$ S m ( T ) ) is observed at very low temperature in magnetically frustrated systems as a consequence of the constraint ( $$S_\mathrm{m}\ge 0$$ S m ≥ 0 ) imposed by the Nernst postulate. The lack of magnetic order allows to explore and compare new thermodynamic properties by tracing the specific heat ( $$C_\mathrm{m}$$ C m ) behavior down to the sub-Kelvin range. Some of the most relevant findings are: (i) a common $$C_\mathrm{m}/T|_{T\rightarrow 0} \approx 7$$ C m / T | T → 0 ≈ 7 J/mol K $$^2$$ 2 ‘plateau’ in at least five Yb-based very-heavy-fermions (VHF) compounds; (ii) quantitative and qualitative differences between VHF and standard non-Fermi-liquids; (iii) entropy bottlenecks governing the change of $$S_\mathrm{m}(T)$$ S m ( T ) trajectories in a continuous transition into alternative ground states. A comparative analysis of $$S_\mathrm{m}(T\rightarrow 0)$$ S m ( T → 0 ) dependencies is performed in compounds suitable for adiabatic demagnetization processes according to their $$\partial ^2 S_\mathrm{m}/\partial T^2$$ ∂ 2 S m / ∂ T 2 derivatives.