The Area-law of Molecular Entropy: Moving Beyond Harmonic Approximation

Abstract Inspired by black hole thermodynamics, the area law that entropy is proportional to horizon area has been proposed in quantum entanglement entropy and has largely maintained its validity. This article shows that the area law is also valid for the thermodynamic entropy of molecules. We showed that the gas-phase entropy of molecules obeys the area law with our proposed correction for the different curvatures of the molecular surface. The coefficient for the ultraviolet cutoff for the molecular entropy, calculated from our curated experimental data, is tantalizingly close to the value $\frac{1}{4}$ proposed by Hawking [Hawking, 1976]. The ability to estimate gas-phase entropy by the area law also allows us to calculate molecular entropy faster and more accurately than currently popular methods of estimating molecular entropy with harmonic oscillator approximation. The speed and accuracy of our method will open up new possibilities for the explicit inclusion of entropy in various computational biology methods.