Thermodynamics of superconducting ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$ in the critical fluctuation region near the ${\mathit{H}}_{\mathit{c}2}$(T) line

We report a detailed study of the temperature and magnetic-field dependence of free energy, magnetization, and specific heat of superconducting ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$ in the critical fluctuation region near ${\mathit{H}}_{\mathit{c}2}$(T) line. Our approach is to apply the recently developed nonperturbative scaling theory (Tešanović et al.) in high fields to describe the reversible magnetization data taken on a c-axis-oriented superconducting ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$ thin tape. We find good agreement on some of the superconducting parameters obtained in the present study with those derived by applying the Ginzburg-Landau theory to our reversible magnetization data taken outside the critical fluctuation region.