# How to measure the entropy of a mesoscopic system via thermoelectric transport

## TL;DR

This paper introduces a method to measure the entropy of mesoscopic systems through thermoelectric transport, providing analytical proof, numerical validation, and experimental application to quantum dots, revealing entropy changes and resolving longstanding puzzles.

## Contribution

It proposes a novel technique to extract entropy from transport measurements in mesoscopic systems, applicable to systems with arbitrary spectra and degeneracies.

## Key findings

- Method successfully applied to quantum dot thermoelectric data
- Able to determine entropy changes across Coulomb-blockade valleys
- Resolves the puzzle of finite thermoelectric response at particle-hole symmetry

## Abstract

Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states, its measurement in such small electron-number system is a daunting task. Here we propose a method to extract the entropy of a Coulomb-blockaded mesoscopic system from transport measurements. We prove analytically and demonstrate numerically the applicability of the method to such a mesoscopic system of arbitrary spectrum and degeneracies. We then apply our procedure to measurements of thermoelectric response of a single quantum dot, and demonstrate how it can be used to deduce the entropy change across Coulomb-blockade valleys, resolving, along the way, a long-standing puzzle of the experimentally observed finite thermoelectric response at the apparent particle-hole symmetric point.