# Direct Entropy Measurement in a Mesoscopic Quantum System

## TL;DR

This paper introduces a novel mesoscopic circuit that directly measures the entropy of a few electrons, providing a new tool for probing quantum states in small systems with high precision.

## Contribution

The authors develop and demonstrate a technique for directly measuring entropy in mesoscopic quantum systems, enabling insights into quantum states that are difficult to access with traditional methods.

## Key findings

- Successfully measured the entropy of a single electron spin with 5% accuracy.
- Validated the method using known spin states in a GaAs quantum dot.
- Potential to distinguish exotic quantum states through entropy measurements.

## Abstract

The entropy of an electronic system offers important insights into the nature of its quantum mechanical ground state. This is particularly valuable in cases where the state is difficult to identify by conventional experimental probes, such as conductance. Traditionally, entropy measurements are based on bulk properties, such as heat capacity, that are easily observed in macroscopic samples but are unmeasurably small in systems that consist of only a few particles. In this work, we develop a mesoscopic circuit to directly measure the entropy of just a few electrons, and demonstrate its efficacy using the well understood spin statistics of the first, second, and third electron ground states in a GaAs quantum dot. The precision of this technique, quantifying the entropy of a single spin-$\frac{1}{2}$ to within 5\% of the expected value of $k_B \ln{2}$, shows its potential for probing more exotic systems. For example, entangled states or those with non-Abelian statistics could be clearly distinguished by their low-temperature entropy.