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The in-plane and out-of-plane superconducting stiffness appear to vanish atdifferent transition temperatures, which contradicts thermodynamicalexpectation. In addition, we observe a surprisingly strong dependence of theout-of-plane stiffness transition on sample width. With evidence from MonteCarlo simulations, this effect is explained by a crossover from threedimensions into quasi one dimensional behavior of the finite sample. Due to anessential singularity at the thermodynamic transition temperature $T_c$, theout-of-plane stiffness appears to vanish below $T_c$ by an amount which isproportional to the inverse width. A fit of our prediction to the data is usedto determine the value of the anisotropy parameter. Analogy to studies ofhelium superfluids in nanopores is made.

The two critical temperatures conundrum in La$_{1.83}$Sr$_{0.17}$CuO$_4$