Thermodynamic reversibility in the superconducting fluctuation regime

Free-energy surfaces derived from magnetization data for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ have been measured in the fluctuation region near the transition temperature in order to determine whether the specific heat derived from magnetization data is the same as the specific heat derived from direct measurements. For ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, there is close agreement and thermodynamic relations apply well even though totally different samples were used. For ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$ and ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$, there is qualitative agreement with direct measurements, but the specific-heat data were taken on a mixed-phase sample.