Background Physics -- Thermodynamic Measurements of Entropy -- Design and Characterisation of Novel Experimental Setup -- Experimental Results and Discussion -- Conclusions and Future Work -- Appendices.

The compound Sr3Ru2O7 of the strontium ruthenate family has been intensely studied because experimental evidence suggests that quantum fluctuations dominate the magnetic phase diagram in the vicinity of a novel low-temperature phase. In order to understand the interplay between the quantum critical fluctuations and the phase formation, comprehensive thermodynamic information is essential. This thesis reports the results of both specific-heat and magnetocaloric experiments carried out with a bespoke experimental apparatus whose design particularly addresses the demanding constraints of the low-temperature, high-magnetic-field environment. The experimental data give evidence for unusual thermodynamic properties of the novel phase and its bounding phase transitions. Furthermore they show that the phase formation takes place against a background of strongly peaking entropy, suggesting that quantum criticality plays a key role in the physics of this system.