The quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production. Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum relaxation processes, strongly depends on the drive-to-decay ratio and the initial state. Furthermore, we carry out experimental verification of this information-theoretical bound by means of a single spin embedded in an ultracold trapped ${}^{40}\mathrm{Ca}^{+}$ ion. Our finding, based on a two-level model, is fundamental to any quantum thermodynamical process and indicates much difference and complexity in quantum thermodynamics with respect to the conventionally classical counterpart.

• Received 24 March 2020
• Revised 23 May 2020
• Accepted 30 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033082

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society