Current Trends in Finite‐Time Thermodynamics

Andresen, Bjarne

doi:10.1002/anie.201001411

Cited by 419 publications

(218 citation statements)

References 266 publications

(182 reference statements)

Supporting

Mentioning

218

Contrasting

Order By: Relevance

“…There has been much discussion about the energy conversion efficiency at the optimal operating point of an endoreversible heat engine and an exo-reversible heat engine [24][25][26][27][28][29][30][31][32][33][34][35]. In particular, Apertet et al [28] developed an empirical model of a thermoelectric generator and then compared the impact of internal and external irreversibilities on the conversion efficiency at the optimal point where the electrical power is maximized.…”

Section: Introductionmentioning

confidence: 99%

Association of Finite-Dimension Thermodynamics and a Bond-Graph Approach for Modeling an Irreversible Heat Engine

Dong

El-Bakkali

Feidt

et al. 2012

Entropy

View full text Add to dashboard Cite

Abstract:In recent decades, the approach known as Finite-Dimension Thermodynamics has provided a fruitful theoretical framework for the optimization of heat engines operating between a heat source (at temperature T hs ) and a heat sink (at temperature T cs ). We will show in this paper that the approach detailed in a previous paper [1] can be used to analytically model irreversible heat engines (with an additional assumption on the linearity of the heat transfer laws). By defining two dimensionless parameters, the intensity of internal dissipation and heat leakage within a heat engine were quantified. We then established the analogy between an endoreversible heat engine and an irreversible heat engine by using the apparent temperatures (T cs → T λ,φ cs , T hs → T

show abstract

Section: Introductionmentioning

confidence: 99%

Association of Finite-Dimension Thermodynamics and a Bond-Graph Approach for Modeling an Irreversible Heat Engine

Dong

El-Bakkali

Feidt

et al. 2012

Entropy

View full text Add to dashboard Cite

show abstract

“…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] is a well established research field which is focused on this issue and in particular on the tradeoff between efficiency and power of realistic heat engines. Several results in this context have been derived from the geometrical notion of thermodynamic length [9], from non-equilibrium identities known as fluctuation theorems [10,11], or from phenomenological models of heat engines [7,14].…”

mentioning

confidence: 99%

Slow Dynamics and Thermodynamics of Open Quantum Systems

2017

View full text Add to dashboard Cite

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]...

show abstract

“…As stated above, although a large body of research focused on maximizing power output or minimizing entropy production for finite-time processes, the selection of the objective function to optimize is not unique and may depend on one's own judgement [10]. The ecological function [8] and the trade-off function [9] are two examples.…”

Section: Unified Approach To Optimizing Generic Objective Functions Bmentioning

confidence: 99%

“…Besides the power output, there are other suggested objective functions such as (i) the so-called ecological function [8], which is defined as P − T c σ, where P is the power output and σ is the entropy production rate of the two heat reservoirs, and the associated efficiency when the ecological function is optimized is well approximated as (η C + η CA )/2 for endoreversible Carnot engines; (ii) a trade-off function [9], which is defined to be proportional to ηP with η being the thermodynamic efficiency, and for low-dissipation engines the corresponding efficiency at maximum trade-off is in the range [2η C /3, (3 − 9 − 8η C )/2]. In fact, the choice of the objective function is somewhat arbitrary, but typically, the objective function is a combination of P, σ, and η, and the corresponding optimized process lies somewhere in the range between the quasistatic process with no dissipation and the process with maximum power output [10].…”

Section: Introductionmentioning

confidence: 99%

Unified Approach to Thermodynamic Optimization of Generic Objective Functions in the Linear Response Regime

Wang

2016

Entropy

View full text Add to dashboard Cite

While many efforts have been devoted to optimizing the power output for a finite-time thermodynamic process, thermodynamic optimization under realistic situations is not necessarily concerned with power alone; rather, it may be of great relevance to optimize generic objective functions that are combinations of power, entropy production, and/or efficiency. One can optimize the objective function for a given model; generally the obtained results are strongly model dependent. However, if the thermodynamic process in question is operated in the linear response regime, then we show in this work that it is possible to adopt a unified approach to optimizing the objective function, thanks to Onsager's theory of linear irreversible thermodynamics. A dissipation bound is derived, and based on it, the efficiency associated with the optimization problem, which is universal in the linear response regime and irrespective of model details, can be obtained in a unified way. Our results are in good agreement with previous findings. Moreover, we unveil that the ratio between the stopping time of a finite-time process and the optimized duration time plays a pivotal role in determining the corresponding efficiency in the case of linear response.

show abstract

Current Trends in Finite‐Time Thermodynamics

Cited by 419 publications

References 266 publications

Association of Finite-Dimension Thermodynamics and a Bond-Graph Approach for Modeling an Irreversible Heat Engine

Association of Finite-Dimension Thermodynamics and a Bond-Graph Approach for Modeling an Irreversible Heat Engine

Slow Dynamics and Thermodynamics of Open Quantum Systems

Unified Approach to Thermodynamic Optimization of Generic Objective Functions in the Linear Response Regime

Contact Info

Product

Resources

About