Experimental study of the thermodynamic uncertainty relation

TL;DR

This paper experimentally investigates the thermodynamic uncertainty relation in a quantum two-qubit system, confirming some theoretical bounds and revealing regimes where tighter bounds are violated, thus deepening understanding of quantum heat exchange.

Contribution

It provides the first experimental validation of the TUR in a quantum system using NMR, and explores the validity of generalized and specialized TUR bounds.

Findings

Generalized TURs are obeyed in the experiment.

Specialized TURs are violated in certain regimes.

The study enhances understanding of heat exchange in quantum systems.

Abstract

A cost-precision trade-off relationship, the so-called thermodynamic uncertainty relation (TUR), has been recently discovered in stochastic thermodynamics. It bounds certain thermodynamic observables in terms of the associated entropy production. In this work, we experimentally study the TUR in a two-qubit system using an NMR setup. Each qubit is prepared in an equilibrium state, but at different temperatures. The qubits are then coupled, allowing energy exchange (in the form of heat). Using the quantum state tomography technique we obtain the moments of heat exchange within a certain time interval and analyze the relative uncertainty of the energy exchange process. We find that generalized versions of the TUR, which are based on the fluctuation relation, are obeyed. However, the specialized TUR, a tighter bound that is valid under specific dynamics, is violated in certain regimes of operation, in excellent agreement with analytic results. Altogether, this experiment-theory study provides a deep understanding of heat exchange in quantum systems, revealing favorable noise-dissipation regimes of operation.