Apparent double-$T_c$ from a single BKT transition in anisotropic phase-only models

Transport experiments on two-dimensional superconductors often yield direction-dependent transition temperatures, raising the question of whether such a ``double-$T_c$’’ reflects a true thermodynamic splitting or a transport artifact. To establish a baseline, we study a minimal anisotropic phase-only Josephson-junction array in equilibrium and under resistively shunted junction dynamics with fluctuating twist boundary conditions. The equilibrium model exhibits a single Berezinskii–Kosterlitz–Thouless (BKT) transition. Out of equilibrium, anisotropic Josephson couplings and anisotropic dissipation reshape the linear $R$–$T$ curves in a finite-size, finite-current crossover regime, so that curve-shape criteria such as Halperin–Nelson fits and fixed-resistance thresholds yield an apparent double-$T_c$. In contrast, critical-scaling criteria – the universal exponent $\alpha =3$ and dynamic finite-size scaling – remain consistent with the single $T_{\mathrm{B}\mathrm{K}\mathrm{T}}$. A robust splitting that persists in the nonlinear critical scaling, such as that recently reported at KTaO${}_3$ interfaces, therefore points to physics beyond this clean anisotropic baseline.