Measuring Topological entanglement entropy using Maxwell relation

Topological entanglement entropy (TEE) is a key diagnostic of topological order, allowing to detect the presence of Abelian or non-Abelian anyons. However, there are currently no protocols to measure TEE in condensed matter systems. We propose a scheme to  measure the TEE, based on a nontrivial connection with the thermodynamic entropy change occurring in a quantum point contact (QPC) as it pinches off the topological liquid into two. We show how this entropy change can be extracted using Maxwell relations from charge detection of a nearby quantum dot. We demonstrate this explicitly for the Abelian Laughlin states, using an exact solution of the  sine-Gordon model describing the universal crossover in the QPC. Our approach might open a new thermodynamic detection scheme of topological states also with non-Abelian statistics. On the experimental side, there has been some remarkable progress in the last few years in measuring thermodynamic entropy in nano- to meso- scale systems. The scheme that we propose to measure TEE is within the reach of current experimental techniques.