Fully Quantum Fluctuation Theorems

Åberg, Johan

doi:10.1103/physrevx.8.011019

Cited by 130 publications

(169 citation statements)

References 194 publications

(473 reference statements)

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“…This contrasts with the TPM approach, in equation (7), which shows the validity of the (classical) Jarzynski equality for an initial thermal state and any choice of time-dependent Hamiltonians [8]. This result demonstrates that when extending fluctuation relations to the quantum regime modifications can arise from coherences, as has been suggested previously [47,25]. We note that the derivation of inequality (26) assumes an initial thermal state, contrasting with previous discussions of quantum signatures in the average exponentiated work by Allhaverdyan, Solinas et al and Elouard et al that have focussed on nonthermal initial states [10,12,35].…”

Section: R Rmentioning

confidence: 58%

Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

Miller

Anders

2017

New J. Phys.

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A central topic in the emerging field of quantum thermodynamics is the definition of thermodynamic work in the quantum regime. One widely used solution is to define work for a closed system undergoing non-equilibrium dynamics according to the two-point energy measurement scheme. However, due to the invasive nature of measurement the two-point quantum work probability distribution cannot describe the statistics of energy change from the perspective of the system alone. We here introduce the quantum histories framework as a method to characterise the thermodynamic properties of the unmeasured, closed dynamics. Constructing continuous power operator trajectories allows us to derive an alternative quantum work distribution for closed quantum dynamics that fulfils energy conservation and is time-reversal symmetric. This opens the possibility to compare the measured work with the unmeasured work, contrasting with the classical situation where measurement does not affect the work statistics. We find that the work distribution of the unmeasured dynamics leads to deviations from the classical Jarzynski equality and can have negative values highlighting distinctly non-classical features of quantum work.

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Section: R Rmentioning

confidence: 58%

Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

Miller

Anders

2017

New J. Phys.

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“…Describing work fluctuations in genuinely coherent processes remains a subtle and open question in quantum thermodynamics, although relevant progress has been achieved recently [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][38][39][40]. Here we report the first experimental observation of work distributions, or, more precisely of transition probabilities, using an implementation based on a CM scheme [18].…”

Section: Discussionmentioning

confidence: 99%

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

Yuan

Xiang

et al. 2019

Sci. Adv.

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In quantum thermodynamics, the standard approach to estimating work fluctuations in unitary processes is based on two projective measurements, one performed at the beginning of the process and one at the end. The first measurement destroys any initial coherence in the energy basis, thus preventing later interference effects. To decrease this back action, a scheme based on collective measurements has been proposed by Perarnau-Llobetet al. Here, we report its experimental implementation in an optical system. The experiment consists of a deterministic collective measurement on two identically prepared qubit states, encoded in the polarization and path degree of a single photon. The standard two-projective measurement approach is also experimentally realized for comparison. Our results show the potential of collective schemes to decrease the back action of projective measurements, and capture subtle effects arising from quantum coherence.

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“…Our results may be of particular importance in setups allowing environmental monitoring and feedback control [50,51,[62][63][64][65][66][67], and for quantum thermal devices working in nonequilibrium steady-state conditions [68][69][70][71][72][73][74][75]. It would be also interesting to explore connections with path-integral approaches [76], one-shot quantum thermodynamics [77][78][79][80], and quantum information [81][82][83][84][85]. Finally, we remark that some of our results could be applied to classical systems where knowledge of system's state is incomplete e.g.…”

mentioning

confidence: 71%

Quantum Martingale Theory and Entropy Production

2019

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We employ martingale theory to describe fluctuations of entropy production for open quantum systems in nonequilbrium steady states. Using the formalism of quantum jump trajectories, we identify a decomposition of entropy production into an exponential martingale and a purely quantum term, both obeying integral fluctuation theorems. An important consequence of this approach is the derivation of a set of genuine universal results for stopping-time and infimum statistics of stochastic entropy production. Finally we complement the general formalism with numerical simulations of a qubit system. PACS numbers: 05.70.Ln, 05.40.-a 05.30.-d 03.67.-a 42.50.DvThe development of stochastic thermodynamics in the last decades allowed the description of work, heat and entropy production at the level of single trajectories in nonequilibrium processes [1,2]. This framework has successfully provided several genuine insights on the second law, such as the discovery of universal relations constraining the statistics of fluctuating thermodynamic quantities, usually known as fluctuation theorems [3][4][5]. The fundamental interest in refining our understanding of irreversibility and their microscopic imprints has been brought to its ultimate consequences by extending stochastic thermodynamics to the quantum realm [6], where fluctuation theorems have been derived [7][8][9][10][11][12][13], and experimentally tested in the last years [14,15].When information about entropy production in single trajectories of a process is available, a natural question to ask is until what extend this information can be useful. For instance whether or not it is possible to implement strategies leading to a reduction in entropy which might be eventually used as a fuel, like in the celebrated Maxwell's demon [16,17]. In the same context, one may ask whether the second law of thermodynamics will manifest as fundamental constraints limiting such strategies. A powerful method to handle these general questions, is to employ a set of particularly interesting stochastic processes, namely Martingales [18]. Martingales are well known in mathematics [19] and quantitative finance as models of fair financial markets [20]. However, martingale theory has been only little exploited until now both in stochastic thermodynamics [21][22][23][24][25][26][27] and quantum physics [28,29].Applying concepts of martingale theory in stochastic thermodynamics, it has been shown that the exponential of minus the entropy production ∆S tot (t) associated with classical trajectories γ {0,t} −single paths in phase space− in generic non-equilibrium steady-state conditions is an exponential martingale, i.e. e −∆Stot(t) | γ {0,τ } = * gmanzano@ictp.it † edgar@ictp.it e −∆Stot(τ ) , for any t ≥ τ ≥ 0, where X(t)|γ {0,τ } denotes the conditional expectation of a functional X(t) given γ {0,τ } [19]. It has been shown that the martingality of e −∆Stot(t) implies a series of universal equalities and inequalities concerning the statistics of infima and stopping times (e.g. first-passage, escape ti...

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Fully Quantum Fluctuation Theorems

Cited by 130 publications

References 194 publications

Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

Experimentally reducing the quantum measurement back action in work distributions by a collective measurement

Quantum Martingale Theory and Entropy Production

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