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

The in-plane and out-of-plane superconducting stiffness appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by a crossover from three dimensions into quasi one dimensional behavior of the finite sample. Due to an essential singularity at the thermodynamic transition temperature $T_c$, the out-of-plane stiffness appears to vanish below $T_c$ by an amount which is proportional to the inverse width. A fit of our prediction to the data is used to determine the value of the anisotropy parameter. Analogy to studies of helium superfluids in nanopores is made.