Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level

Alexandre M. Souza; Gabriele De Chiara; Ivan S. Oliveira; John Goold; Laura Mazzola; Mauro Paternostro; Roberto M. Serra; Ruben Auccaise; Tiago Batalh\~ao

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Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level

Tiago Batalhão, Alexandre M. Souza, Laura Mazzola, Ruben Auccaise, Ivan S. Oliveira, John Goold, Gabriele De Chiara, Mauro Paternostro

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Roberto M. Serra

Quantum Physics · Submitted 14 Aug 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, by exploiting a radical change in the characterization of the work distribution at the quantum level, we report the first experimental verification of the quantum Jarzynski identity and the Tasaki-Crooks relation following a quantum process implemented in a Nuclear Magnetic Resonance (NMR) system.

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arXiv ID1308.3241 (version 1)

Pith IDXLPE6357, Pith's permanent record of this paper and its review

CitationAlexandre M. Souza, Gabriele De Chiara, Ivan S. Oliveira, John Goold, Laura Mazzola, Mauro Paternostro, Roberto M. Serra, Ruben Auccaise, Tiago Batalh\~ao. "Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level." arXiv:1308.3241 (2013). https://pith.science/paper/XLPE6357

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What the abstract itself states, as probabilities: claims first 0.91 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.77 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Research on the out-of-equilibrium dynamics of quantum systems has so far produced important statements on the thermodynamics of small systems undergoing quantum mechanical evolutions. Key examples are provided by the Crooks and Jarzynski relations: taking into account fluctuations in non-equilibrium dynamics, such relations connect equilibrium properties of thermodynamical relevance with explicit non-equilibrium features. Although the experimental verification of such fundamental relations in the classical domain has encountered some success, their quantum mechanical version requires the assessment of the statistics of work performed by or onto an evolving quantum system, a step that has so far encountered considerable difficulties in its implementation due to the practical difficulty to perform reliable projective measurements of instantaneous energy states. In this paper, by exploiting a radical change in the characterization of the work distribution at the quantum level, we report the first experimental verification of the quantum Jarzynski identity and the Tasaki-Crooks relation following a quantum process implemented in a Nuclear Magnetic Resonance (NMR) system. Our experimental approach has enabled the full characterisation of the out-of-equilibrium dynamics of a quantum spin in a statistically significant way, thus embodying a key step towards the grounding of quantum-systems thermodynamics.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Research on the out-of-equilibrium dynamics of quantum systems has so far produced important statements on the thermodynamics of small systems undergoing quantum mechanical evolutions.	background 1.00	0.04	0.02	asserted 1.00
s1	Key examples are provided by the Crooks and Jarzynski relations: taking into account fluctuations in non-equilibrium dynamics, such relations connect equilibrium properties of thermodynamical relevance with explicit non-equilibrium features.	background 1.00	0.04	0.03	asserted 1.00
s2	Although the experimental verification of such fundamental relations in the classical domain has encountered some success, their quantum mechanical version requires the assessment of the statistics of work performed by or onto an evolving quantum system, a step that has so far encountered considerable difficulties in its implementation due to the practical difficulty to perform reliable projective measurements of instantaneous energy states.	gap 0.89	0.04	0.03	asserted 0.99
s3	In this paper, by exploiting a radical change in the characterization of the work distribution at the quantum level, we report the first experimental verification of the quantum Jarzynski identity and the Tasaki-Crooks relation following a quantum process implemented in a Nuclear Magnetic Resonance (NMR) system.	contribution 0.81	0.97	0.91	asserted 1.00
s4	Our experimental approach has enabled the full characterisation of the out-of-equilibrium dynamics of a quantum spin in a statistically significant way, thus embodying a key step towards the grounding of quantum-systems thermodynamics.	interpretation 0.94	0.96	0.38	asserted 0.98

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

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arXiv listing abstract v1

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full text
figures and tables
references and citing sentences
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P abstract

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The paper

Original abstract

Research on the out-of-equilibrium dynamics of quantum systems has so far produced important statements on the thermodynamics of small systems undergoing quantum mechanical evolutions. Key examples are provided by the Crooks and Jarzynski relations: taking into account fluctuations in non-equilibrium dynamics, such relations connect equilibrium properties of thermodynamical relevance with explicit non-equilibrium features. Although the experimental verification of such fundamental relations in the classical domain has encountered some success, their quantum mechanical version requires the assessment of the statistics of work performed by or onto an evolving quantum system, a step that has so far encountered considerable difficulties in its implementation due to the practical difficulty to perform reliable projective measurements of instantaneous energy states. In this paper, by exploiting a radical change in the characterization of the work distribution at the quantum level, we report the first experimental verification of the quantum Jarzynski identity and the Tasaki-Crooks relation following a quantum process implemented in a Nuclear Magnetic Resonance (NMR) system. Our experimental approach has enabled the full characterisation of the out-of-equilibrium dynamics of a quantum spin in a statistically significant way, thus embodying a key step towards the grounding of quantum-systems thermodynamics.

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137 later papers cite it

Evidence: substantial. 111 of the citing papers share no author with it, and 8 of those carry a confident label from Pith's citation classifier.

Pith read 11 of the 201 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

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We extracted the data for the validation from Fig. 3 of Ref. [ref] , from Fig. 3 of Ref. [ref] , from Fig. 3 of Ref. [ref] , Fig. 3 of Ref. [ref] and Table 1 of [ref] .

Quantum many-body Jarzynski equality and dissipative noise on a digital quantum computer (2022) · Comparison with previous experiments · 0.95

How the literature uses it

20 arXiv papers cite this in 33 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 25 sentences without a confident label

Uses its method or tool 1 paper

The heat distribution and its moments may then be extracted via an anti-Fourier transform of this signal [ref] .

Measuring the heat exchange of a quantum process · Introduction · 0.94

Cites it as background 5 papers

One important area within this field, which has received a large amount of recent attention, is the development of experimental techniques and protocols which can test the theoretical predictions [ref] .

Organic molecule fluorescence as an experimental test-bed for quantum jumps in thermodynamics · Introduction · 0.85
Recent discussions [ref] are focused on the Crooks FR [ref] for a driven qubit.

Distribution of energy dissipated by a driven two-level system · Introduction · 0.95
Extensions to the quantum regime are reviewed in [ref] and the first quantum experiments using nuclear magnetic resonance are reported in [ref] .

Jarzynski equality for a gas particle driven out of equilibrium · Introduction · 0.93

What it cites · 2 sentences without a confident label

Cites as background 3 papers

The verification and use of quantum fluctuation relations [ref] requires the design of experimentally feasible strategies for the determination of the work distribution following a process undergone by a system.

Jarzynski Relations for Quantum Systems and Some Applications · Introduction · 0.92
Albeit a few proposals for the measurement of the quantum statistics of work have been made [ref] , including an ingenious calorimetric one [ref] , the experimental reconstruction of either $P_α(W)$ or $χ_α(u)$ has been hindered by the technical difficulties inherent in the determination of the conditional probabilities $p^τ_m|n$.

Calorimetric measurement of quantum work · Introduction · 0.92
It is well-known that unitality is the quantum counterpart of classical microreversibility [ref] .

Fluctuation theorems for quantum processes · Micro-reversibility · 0.87

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