Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink

Johal, Ramandeep S.; Rai, Renuka

doi:10.1209/0295-5075/113/10006

Cited by 17 publications

(33 citation statements)

References 28 publications

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“…1 and 1/8) are independent of α and correspond to the same values in the Taylor expansion of the CurzonAhlborn [14,21] and of the Schmiedl-Seifert [18] efficiencies. This also implies that, up to second order in η C , our results are in agreement with previous analyses based on linear response thermodynamics [7,29]. Conclusions and outlook.-We have derived a perturbation theory for the solution of generic master equations with slowly varying coefficients.…”

Section: ρ(T) = L T [ρ(T)]supporting

confidence: 90%

“…The impact of the bath spectral density on the efficiency of quantum engines was also noticed in the context of autonomous heat pumps [24,25] and single-qubit minimal machines [26]. Universal features and bounds for the efficiency at maximum power of finite-time Carnot cycles were identified in [18,[27][28][29] for generic heat engines. Other results were obtained combining MMEs and linear response theory [7,30,31] and similar approaches were used to demonstrate the universality of heat engines in the limit of infinitesimal cycles [32].…”

Section: ρ(T) = L T [ρ(T)]mentioning

confidence: 81%

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Slow Dynamics and Thermodynamics of Open Quantum Systems

2017

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We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasi-static transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated to an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.A central result in the study of open quantum systems [1, 2] is the Markovian Master Equation (MME) approach which, under realistic assumptions, describes the temporal evolution of a system of interest A induced by a weak coupling with a large external environment E. This consists in a first order linear differential equatioṅ ρ(t) = L[ρ(t)] where ρ(t) is the density matrix of A and where the generator of the dynamics is provided by a quantum Liouvillian superoperator L that can be casted in the so called Gorini-Kossakowski-Sudarshan-Lindblad form [3][4][5]. For autonomous systems the latter does not exhibit an explicit time dependence and the dynamics of A exponentially relaxes to a (typically unique) equilibrium steady state ρ 0 identified by the null eigenvector equation L[ρ 0 ] = 0. MMEs can also be employed to describe the temporal evolution of A when it is tampered by the presence of slow varying, external driving forces. Indeed, as long as these operate on a time scale which is much larger than the characteristic bath correlations times and the inverse frequencies of the system of interest, the effective coupling between A and E adapts instantaneously to the driving control, resulting on a MME governed by a time-dependent Liouvillian generator, i.e.An explicit integration of this equation is in general difficult to obtain. Yet, if the control forces are so slow that their associated time scale is also larger with respect to the relaxation time of the system induced by the interaction with E, one expects ρ(t) to approximately follow the instantaneous equilibrium state ρ 0 (t) that nullifies L t . Our aim is to estimate quantitative deviations from this ultra-slow driving regime. For this purpose we develop a perturbation theory valid in the limit of slowly varying Liouvillians L t and derive a formal solution of Eq. (1) which allows one to evaluate non-equilibrium corrections up to arbitrary order. The main motivation of our analysis is to model thermodynamic processes and cycles beyond the usual reversible limit which is strictly valid only for infinitely long quasi-static transformations. Finite-time thermodynamics [7,8]...

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Section: ρ(T) = L T [ρ(T)]supporting

confidence: 90%

Section: ρ(T) = L T [ρ(T)]mentioning

confidence: 81%

Slow Dynamics and Thermodynamics of Open Quantum Systems

2017

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“…In practical cases, the engines and other thermodynamic machines work in finite cycle-times. Thus an extension of our analysis within an irreversible framework [5] may help to see how the above conclusions are retained or modified in finite-time models, at least under linear response or beyond that [7]. Another interesting line of enquiry seems to be the connection of the bounds on efficiency with the principles of inductive inference [31,32].…”

Section: Bounds On Efficiencymentioning

confidence: 93%

Optimal performance of heat engines with a finite source or sink and inequalities between means

Johal

2016

Phys. Rev. E

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Given a system with a finite heat capacity and a heat reservoir, and two values of initial temperatures, T + and T − (< T + ), we enquire, in which case the optimal work extraction is larger: when the reservoir is an infinite source at T + and the system is a sink at T − , or, when the reservoir is an infinite sink at T − and the system acts as a source at T + ? It is found that in order to compare the total extracted work, and the corresponding efficiency in the two cases, we need to consider three regimes as suggested by an inequality, the so-called arithmetic mean-geometric mean inequality, involving the arithmetic and the geometric means of the two temperature values T + and T − . In each of these regimes, the efficiency at total work obeys certain universal bounds, given only in terms of the ratio of initial temperatures.The general theoretical results are exemplified for thermodynamic systems for which internal energy and temperature are power laws of the entropy. The conclusions may serve as benchmarks in the design of heat engines, where we can choose the nature of the finite system, so as to tune the total extractable work and/or the corresponding efficiency.

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“…Thus the EMP in this limit is η l = η C /2. This formula is obtained when the dissipation at the cold contact is much more important than at the hot contact [3,7,8,12,28]. In our model, this limit implies that when the effective amount of heat passing through the machine approaches the heat absorbed from the hot reservoir, then the efficiency approaches its lower bound.…”

mentioning

confidence: 91%

“…for small differences in reservoir temperatures, EMP can be written as: η = η C /2 + η 2 C /8 + O[η 3 C ]. The first-order term arises with strong coupling under linear irreversible thermodynamics (LIT) [6], while the second-order term is beyond linear response, and has been related to a certain symmetry property in the model [28,30].…”

mentioning

confidence: 99%

Global linear-irreversible principle for optimization in finite-time thermodynamics

Johal

2018

EPL

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There is intense effort into understanding the universal properties of finite-time models of thermal machines-at optimal performance-such as efficiency at maximum power, coefficient of performance at maximum cooling power, and other such criteria. In this letter, a global principle consistent with linear irreversible thermodynamics is proposed for the whole cycle-without considering details of irreversibilities in the individual steps of the cycle. This helps to express the total duration of the cycle as τ ∝Q 2 /∆ tot S, whereQ models the effective heat transferred through the machine during the cycle, and ∆ tot S is the total entropy generated. By takingQ in the form of simple algebraic means (such as arithmetic and geometric means) over the heats exchanged by the reservoirs, the present approach is able to predict various standard expressions for figures of merit at optimal performance, as well as the bounds respected by them. It simplifies the optimization procedure to a oneparameter optimization, and provides a fresh perspective on the issue of universality at optimal performance, for small difference in reservoir temperatures. As an illustration, we compare performance of a partially optimized four-step endoreversible cycle with the present approach. * rsjohal@iisermohali.ac.in

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Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink

Cited by 17 publications

References 28 publications

Slow Dynamics and Thermodynamics of Open Quantum Systems

Slow Dynamics and Thermodynamics of Open Quantum Systems

Optimal performance of heat engines with a finite source or sink and inequalities between means

Global linear-irreversible principle for optimization in finite-time thermodynamics

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