Abstract
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 $^{40}$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.
Highlights
Unitary operations, demonstrating reversibility, are the key concept in every textbook of quantum mechanics
The two-level system could be initialized in a state involving coherence, rather than a well-polarized state, for which we present below that Eq (1) is not always valid for most drive-to-decay ratio (DDR) values
We explored a quantum mechanical informationtheoretical bound of irreversibility using a fundamental two-level system, which applies to any quantum thermodynamic process
Summary
Unitary operations, demonstrating reversibility, are the key concept in every textbook of quantum mechanics. The fluctuation theorem has derived the result of nonnegativity of the entropy production, i.e., the essence of the SLT. Based on this idea, some recent publications [5,6,7,8,9] tried to develop theories to further understand the thermodynamic irreversibility inherent to nonequilibrium processes. A very recent work focusing on thermal relaxation processes acquired an information-theoretical bound of irreversibility [10], which imposes a stronger constraint on the entropy production than the conventional SLT. We explore, both theoretically and experimentally, the information-theoretical bound of irreversibility studied classical mechanically in [10], in the quantum regime. By precisely manipulating a single ultracold trapped 40Ca+ ion, we demonstrate experimentally a single-spin verification of this bound, witnessing the predicted violation
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