Measuring topological entanglement entropy using Maxwell relation

Topological entanglement entropy (TEE) is an important characteristic of topological order, but there is currently no protocol to measure it experimentally. There exists a nontrivial connection between TEE and thermodynamic entropy: in a point contact formed between the edge states of a topological phase, the thermodynamic entropy change between the ultraviolet (weak backscattering) and infrared (strong backscattering) fixed points equals the TEE. We propose a protocol to experimentally measure this change in the thermodynamic entropy, and thereby measure TEE, by making use of a Maxwell relation. We illustrate how the proposed TEE measurement would work for the experimentally relevant fractional quantum Hall case with filling factor 1/3.