Current-constraining variational approaches to quantum transport

Bokes, P.; Mera, H.; Godby, R. W.

doi:10.1103/physrevb.72.165425

Cited by 13 publications

(14 citation statements)

References 33 publications

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“…An alternative form for the NESS statistical operator was derived in the 90's by Hershfield 41 using a scattering-theory based approach. Not only are the approaches known to be equivalent [46][47][48] but they can also can be obtained from a max-entropy approach 49,50 , analogous to equilibrium ensembles 51,52 , but with constrained finite currents.…”

Section: Non-equilibrium Steady-state Statistical Operatormentioning

confidence: 99%

Thermodynamics of precision in quantum nonequilibrium steady states

Guarnieri

Landi

Clark

et al. 2019

Phys. Rev. Research

167

111

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Autonomous engines operating at the nano-scale can be prone to deleterious fluctuations in the heat and particle currents which increase, for fixed power output, the more reversible the operation regime is. This fundamental trade-off between current fluctuations and entropy production forms the basis of the so-called thermodynamic uncertainty relations (TURs). Importantly, recent studies have shown that they can be violated in the quantum regime, thus motivating the search for analogous quantum counterparts. In this paper we show that the geometry of quantum non-equilibrium steady-states alone directly implies the existence of TUR, but with a looser bound, which is not violated by the above recent findings. The geometrical nature of this result makes it extremely general, establishing a fundamental limit for the thermodynamics of precision. Our proof is based on the McLennan-Zubarev ensemble, which provides an exact description of non-equilibrium steady-states. We first prove that the entropy production of this ensemble can be expressed as a quantum relative entropy. The TURs are then shown to be a direct consequence of the Cramer-Rao bound, a fundamental result from parameter estimation theory. By combining techniques from many-body physics and information sciences, our approach also helps to shed light on the delicate relationship between quantum effects and current fluctuations in autonomous machines, where new general bound on the power output are found and discussed.

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Section: Non-equilibrium Steady-state Statistical Operatormentioning

confidence: 99%

Thermodynamics of precision in quantum nonequilibrium steady states

Guarnieri

Landi

Clark

et al. 2019

Phys. Rev. Research

167

111

View full text Add to dashboard Cite

show abstract

“…Recently, Tasaki and Takahashi also employed asymptotic operators (6) to continue the advances of Zubarev method in application to transport in quantum junctions [24]. The time invariant current defined via (7) was used by Bokes, Mera, and Godby as a term constrained by the Lagrange multiplier in their development of variational transport theory [31]. In this paper, we develop a general practical method for computing asymptotic non-equilibrium operators.…”

Section: Asymptotic Operatorsmentioning

confidence: 99%

Asymptotic nonequilibrium steady-state operators

Gelin

Kosov

2009

Phys. Rev. E

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We present a method for the calculation of asymptotic operators for nonequilibrium steady-state quantum systems. The asymptotic steady-state operator is obtained by averaging the corresponding operator in Heisenberg representation over infinitely long time. Several examples are considered to demonstrate the utility of our method. The results obtained within our approach are compared to those obtained within the Schwinger-Keldysh nonequilibrium Green's functions.

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“…To derive the steady-state distribution, we can also apply the procedure of the external driving of the molecular Hamiltonian. [37,38,39,40,41,42,43,44] Namely, we assume that the system-bath interaction is switched on adiabatically, so that the total time-dependent…”

Section: Classical Systemsmentioning

confidence: 99%

Unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems

Gelin¹,

Kosov²

2008

Phys. Rev. E

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We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and (generalized) free energies through simulations or measurements performed on nonequilibrium systems.

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Current-constraining variational approaches to quantum transport

Cited by 13 publications

References 33 publications

Thermodynamics of precision in quantum nonequilibrium steady states

Thermodynamics of precision in quantum nonequilibrium steady states

Asymptotic nonequilibrium steady-state operators

Unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems

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