Exchange fluctuation theorem for correlated quantum systems

Jevtic, Sania; Rudolph, Terry; Jennings, David; Hirono, Yuji; Nakayama, Shojun; Murao, Mio

doi:10.1103/physreve.92.042113

Cited by 43 publications

(53 citation statements)

References 34 publications

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“…In Ref. [39], an interesting exchange fluctuation theorem is suggested. However, this approach is valid only for systems that are initially in local equilibrium.…”

Section: E Icci For a Coupled Thermal Statementioning

confidence: 99%

“…III we derive additional inequalities that were not obtained in Refs. [37][38][39]. Equation (28) was derived for a setup prepared in a coupled thermal state Eq.…”

Section: E Icci For a Coupled Thermal Statementioning

confidence: 99%

“…While both Eqs. (6) and (39) are Kraus maps, Eq. (39) is not a mixture of unitaries due to the presence of the measurement projectors.…”

Section: Detecting Evasive Feedback Demonsmentioning

confidence: 99%

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Global Passivity in Microscopic Thermodynamics

Uzdin

Rahav

2018

Phys. Rev. X

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The main thread that links classical thermodynamics and the thermodynamics of small quantum systems is the celebrated Clausius inequality form of the second law. However, its application to small quantum systems suffers from two cardinal problems. (i) The Clausius inequality does not hold when the system and environment are initially correlated-a commonly encountered scenario in microscopic setups. (ii) In some other cases, the Clausius inequality does not provide any useful information (e.g., in dephasing scenarios). We address these deficiencies by developing the notion of global passivity and employing it as a tool for deriving thermodynamic inequalities on observables. For initially uncorrelated thermal environments the global passivity framework recovers the Clausius inequality. More generally, global passivity provides an extension of the Clausius inequality that holds even in the presences of strong initial system-environment correlations. Crucially, the present framework provides additional thermodynamic bounds on expectation values. To illustrate the role of the additional bounds, we use them to detect unaccounted heat leaks and weak feedback operations ("Maxwell demons") that the Clausius inequality cannot detect. In addition, it is shown that global passivity can put practical upper and lower bounds on the buildup of system-environment correlations for dephasing interactions. Our findings are highly relevant for experiments in various systems such as ion traps, superconducting circuits, atoms in optical cavities, and more.

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“…In Ref. [39], an interesting exchange fluctuation theorem is suggested. However, this approach is valid only for systems that are initially in local equilibrium.…”

Section: E Icci For a Coupled Thermal Statementioning

confidence: 99%

“…III we derive additional inequalities that were not obtained in Refs. [37][38][39]. Equation (28) was derived for a setup prepared in a coupled thermal state Eq.…”

Section: E Icci For a Coupled Thermal Statementioning

confidence: 99%

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Global Passivity in Microscopic Thermodynamics

Uzdin

Rahav

2018

Phys. Rev. X

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“…It vanishes on average, since the global dynamics is unitary and no extra energy is exchanged with an external bath.Equation (10) is our first main result. It generalizes quantum fluctuation theorems for heat exchange beyond the standard TPM approach [19,20]. To make this point more precise, we express the stochastic quantum mutual informations, I l = J l + C l , (l = 0, 1), as a sum of the stochastic classical mutual information, J l = ln(P a l b l /P a l P b l ), and of the stochastic quantum relative entropy of coherence, C l = ln(P s /P a l b l ), which is a proper measure of quantum coherence in a given basis [28].…”

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confidence: 94%

“…The operator χ AB induces correlations between the two subsystems. It is assumed to satisfy tr i [χ AB ] = 0, so that the reduced states, ρ i (0) = tr j [ρ AB (0)], are locally thermal even though A and B are globally correlated [20]. This condition guarantees arXiv:1909.12189v1 [quant-ph] 26 Sep 2019 2 that the local systems have a well defined temperature.…”

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confidence: 99%

Quantum Fluctuation Theorems beyond Two-Point Measurements

2020

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We derive detailed and integral quantum fluctuation theorems for heat exchange in a quantum correlated bipartite thermal system using the framework of dynamic Bayesian networks. Contrary to the usual two-projective-measurement scheme that is known to destroy quantum features, these fluctuation relations fully capture quantum correlations and quantum coherence at arbitrary times.Fluctuation theorems are fundamental generalizations of the second law of thermodynamics for small systems. While the entropy production Σ is a nonnegative deterministic quantity for macroscopic systems, it becomes random at the microscopic scale owing to the presence of nonnegligible thermal [1,2] or quantum [3,4] fluctuations. Detailed fluctuation theorems quantify the probability of occurrence of negative entropy production events via the general relation P (Σ)/P (−Σ) = exp(Σ) [5]. Integral fluctuation theorems take on the form exp(−Σ) = 1 after integration over Σ. The concavity of the exponential function then implies that the entropy production is only positive on average, Σ ≥ 0. The generic validity of fluctuation theorems arbitrarily far from equilibrium makes them particularly useful in nonequilibrium physics. They have been extensively investigated for this reason, both theoretically and experimentally, for classical systems [6,7]. These studies have provided unique insight into the thermodynamics of microscopic systems, from colloidal particles to enzymes and molecular motors [1,2].The situation is more involved in the quantum regime. Quantum fluctuation theorems are commonly studied within the two-point-measurement (TPM) scheme [3,4]. In this approach, the energy change, and in turn the entropy production, of a quantum system are determined for individual realizations by projectively measuring the energy at the beginning and at the end of a nonequilibrium protocol [8]. Equivalent formulations based on Ramsey-like interferometry [10,11] and generalized measurements [12] have also been proposed. These methods were used to perform experimental tests of quantum fluctuations theorems, both for mechanically driven [13][14][15] and thermally driven [16] systems, using NMR, trappedion and cold-atom setups. The TPM procedure successfully captures the discrete quantum energy spectrum of the system, as well as its nonequilibrium quantum dynamics between the two measurements [9]. However, due to its projective nature, it completely fails to account for quantum correlations and quantum coherence, two central features of quantum theory, that may be present in initial and final states of the system. In that sense, the TPM scheme may thus be viewed as not fully quantum.In this paper, we present detailed and integral quantum fluctuation theorems for heat exchange between quantum correlated bipartite thermal systems using a dynamic Bayesian network approach [17,18]. Global and local descriptions of a composite system usually differ because of quantum correlations. The dynamic Bayesian network offers a powerful framework to specify the local dynam...

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Quantum Thermodynamics

Paule¹

2018

Springer Theses

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Exchange fluctuation theorem for correlated quantum systems

Cited by 43 publications

References 34 publications

Global Passivity in Microscopic Thermodynamics

Global Passivity in Microscopic Thermodynamics

Quantum Fluctuation Theorems beyond Two-Point Measurements

Quantum Thermodynamics

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