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Low-temperature phase transitions and the associated quantum critical points are a major field of research, but one in which experimental information about thermodynamics is sparse. Thermodynamic information is vital for the understanding of quantum many-body problems. We show that combining measurements of the magnetocaioric effect and specific heat allows a comprehensive study of the entropy of a system. We present a quantitative measurement of the entropic landscape of [Sr.sub.3][Ru.sub.2][O.sub.7], a quantum critical system in which magnetic field is used as a tuning parameter. This allows us to track the development of the entropy as the quantum critical point is approached and to study the thermodynamic consequences of the formation of a novel electronic liquid crystalline phase in its vicinity.

Abstract: We present a brief review of the physical properties of Sr3Ru2O7, in which the approach to a magnetic-field-tuned quantum critical point is cut off by the formation of a novel phase with transport characteristics consistent with those of a nematic electronic liquid crystal. Our goal is to summarise the physics that led to that conclusion being drawn, describing the key experiments and discussing the theoretical approaches that have been adopted. Throughout the review we also attempt to highlight observations that are not yet understood, and to discuss the future challenges that will need to be addressed by both experiment and theory. [Copyright &y& Elsevier]