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Sr$_2$RuO$_4$ is an unconventional superconductor whose superconductivity is unusually sensitive to the underlying electronic structure and lattice symmetry. In particular, uniaxial stress provides a direct route to tuning the physics of Sr$_2$RuO$_4$: stress applied along the $\langle 100\rangle$ direction lowers the tetragonal symmetry, modifies the Fermi surface, and drives the system toward a Van Hove singularity, where a strong enhancement of the superconducting transition temperature is observed.
As a strain-sensitive thermodynamic probe, the elastocaloric effect measures the temperature response to an oscillating strain and provides access to entropy derivatives with respect to strain. Li et al. reported a detailed implementation of this technique in Sr$_2$RuO$_4$ (Nature 607, 276–280, 2022), including the first elastocaloric mapping of a strain-tuned superconducting transition. Our analysis shows that the quasi-adiabatic regime used in Li et al. is difficult to maintain across the experimentally relevant phase diagram. To address this limitation and enable quantitative interpretation of the data, we developed an alternative elastocaloric protocol, which we refer to as the strong-coupling regime. In this regime, the sample temperature remains well thermalized to the platform while the measurement retains sensitivity to the strain-induced entropy response. This approach complements the conventional quasi-adiabatic elastocaloric limit and enables accurate thermodynamic extraction under mechanically constrained conditions.
Using ECE data measured in both the strong-coupling and quasi-adiabatic regimes as thermodynamic input, we reconstruct the absolute entropy landscape across the full temperature–strain phase diagram of Sr$_2$RuO$_4$. This combined approach exploits the absolute accuracy of low-frequency strong-coupling measurements together with the high signal-to-noise ratio of high-frequency quasi-adiabatic measurements. The resulting entropy map resolves the thermodynamic signatures associated with the stress-enhanced superconducting transition and enables the quantitative derivation of specific heat throughout the temperature–strain plane. The reconstructed heat capacity reveals no evidence for additional thermodynamically significant phase transitions within the superconducting dome and indicates an enhanced superconducting heat-capacity anomaly near the Van Hove point.