We have recently reported the first direct calorimetric observation of a magnetic-field-induced first-order phase transition into a high-field FFLO superconducting state at the Clogston-Chandrasekar `Pauli paramagnetic limit $H_p$ in a 2D superconductor $kappa-{textrm{(BEDT-TTF)}}_2{textrm{Cu}}{textrm{(NCS)}}_2$. The high-field state is both higher entropy and strongly paramagnetic, as thermodynamically required for the FFLO state. Here we compare our results with theoretical predictions for the field dependence of the high-field FFLO state in the 2D limit, revealing tentative evidence for transitions between FFLO states of differing order parameter. We also present calorimetric evidence for a 1st order phase transition into the FFLO state for a second 2D organic superconductor: ${beta}^{primeprime}-{textrm{(BEDT-TTF)}}_2{textrm{SF}}_5{textrm{(CH)}}_2{textrm{(CF)}}_2{textrm{(SO)}}_3$.
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