The third law of thermodynamics in open quantum systems

Shastry, Abhay; Xu, Yanjin; Stafford, Charles

doi:10.1063/1.5100182

Cited by 8 publications

(4 citation statements)

References 37 publications

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“…, where f α is the Fermi-Dirac function of the reservoir α; f l is the occupation number of the l-th localized state of the system, and ψ l (x) is the wave-function of the l-th localized state. It has been analytically shown in [412][413][414] that the local entropy S (x) asymptotically converges to zero as T * → 0, consistent with the third law of thermodynamics.…”

Section: Implications and Applications Of Non-equilibrium Local Tempe...supporting

confidence: 57%

“…Only one point can be found along I p = 0 that also satisfies J p = 0, which implies a unique result of the ZCC. The Third Law -By carefully defining a local non-equilibrium entropy of a fermionic system in a non-equilibrium steady state, the local temperature has been found to be consistent with the Nernst's statement of the third law [412][413][414], that it is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolutezero value in a finite number of operations [415]. The local non-equilibrium entropy S (x) is defined as follows [414] S…”

Section: Implications and Applications Of Non-equilibrium Local Tempementioning

confidence: 60%

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Local temperatures out of equilibrium

2019

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The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium. Figure 4: (a) The product of the density of states η(E) times the global distribution function ϕ|ρ|ϕ forms a strongly pronounced peak at the expectation value of the global system energyĒ. (b) The logarithm of the local distribution function a|ρ|a (solid line) and the logarithm of a canonical distribution (dashed line) with the same local temperature for a harmonic chain. (a) and (b) are reprinted with permission from [74].

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Section: Implications and Applications Of Non-equilibrium Local Tempe...supporting

confidence: 57%

Section: Implications and Applications Of Non-equilibrium Local Tempementioning

confidence: 60%

Local temperatures out of equilibrium

2019

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“…The mathematical analysis by Belgiorno confirms the Planck version of the 3rd law, lim T→0 + S(T) = 0 [69,70]. According to Shastry et al the third law is also valid in open quantum systems [71]. Steane presented an alternative route to obtaining S(T = 0), without the third law or quantum mechanics [13].…”

Section: Quantum Theory and The Third Lawmentioning

confidence: 92%

Testing the Minimum System Entropy and the Quantum of Entropy

Hohm,

Schiller

2023

Entropy

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Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature.

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“…The discovery of the fact that thermodynamic principles are consistent with the quantum properties of microscopic systems has led to a flurry of research activity in the recent times. Quantum thermodynamics, as the subject is known (see for example [1,2] for a pedagogical introduction), has seen several remarkable recent advances such as the formulation of quantum thermodynamic functions [3][4][5] and the third law (see [6] and references therein), a novel proposal of a quantum analogue of energy equipartition [7][8][9][10][11][12] as well as studies on non-equilibrium steady states in nanoscale systems [13][14][15]. A particularly interesting aspect is that of the quantum counterpart of the classical energy equipartition theorem, which is being actively worked on.…”

Section: Introductionmentioning

confidence: 99%

Partition of free energy for a Brownian quantum oscillator: Effect of dissipation and magnetic field

Kaur,

Ghosh,

Bandyopadhyay

2022

Preprint

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Recently, the quantum counterpart of energy equipartition theorem has drawn considerable attention. Motivated by this, we formulate and investigate an analogous statement for the free energy of a quantum oscillator linearly coupled to a passive heat bath consisting of an infinite number of independent harmonic oscillators. We explicitly demonstrate that the free energy of the Brownian oscillator can be expressed in the form F (T ) = f (ω, T ) where f (ω, T ) is the free energy of an individual bath oscillator. The overall averaging process involves two distinct averages: the first one is over the canonical ensemble for the bath oscillators, whereas the second one signifies averaging over the entire bath spectrum of frequencies from zero to infinity. The latter is performed over a relevant probability distribution function P(ω) which can be derived from the knowledge of the generalized susceptibility encountered in linear response theory. The effect of different dissipation mechanisms is also exhibited. We find two remarkable consequences of our results. First, the quantum counterpart of energy equipartition theorem follows naturally from our analysis. The second corollary we obtain is a natural derivation of the third law of thermodynamics for open quantum systems. Finally, we generalize the formalism to three spatial dimensions in the presence of an external magnetic field.

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The third law of thermodynamics in open quantum systems

Cited by 8 publications

References 37 publications

Local temperatures out of equilibrium

Local temperatures out of equilibrium

Testing the Minimum System Entropy and the Quantum of Entropy

Partition of free energy for a Brownian quantum oscillator: Effect of dissipation and magnetic field

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