Reprint of : Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

The Carnot efficiency enabled by complete degeneracies

Quantum-size effects unavoidably produce imperfect-regeneration heat losses in irreversible isothermal expansion/compression cycles, leading to the less efficiency of micro engines. Here, we design a smallest quantum Stirling-like heat engine using a single trapped electron as the working substance. The quantum probabilities to determine the electronic position are constructed from the incoherent mixed ensemble. When the quantum well expands isothermally to double its size and an infinite delta-function potential barrier is inserted in the middle, the complete degeneracies enable the heat engine to work reversibly and achieve the Carnot efficiency. The proposed theoretical model can open up new avenues for building practical nano-energy devices.     

Efficiency bounds for nonequilibrium heat engines

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples.     

Reversible quantum brownian heat engines for electrons

Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.     

Performance characteristics of low-dissipative generalized Carnot cycles with external leakage losses

Under the assumption of low-dissipation, a unified model of generalized Carnot cycles with external leakage losses is established. Analytical expressions for the power output and efficiency are derived. The general performance characteristics between the power output and the efficiency are revealed. The maximum power output and efficiency are calculated. The lower and upper bounds of the efficiency at the maximum power output are determined. The results obtained here are universal and can be directly used to reveal the performance characteristics of different Carnot cycles, such as Carnot heat engines, Carnot-like heat engines, flux flow engines, gravitational engines, chemical engines, two-level quantum engines,etc.     

带有Dzyaloshinski-Mariya相互作用的两比特纠缠量子Otto热机和量子Stirling热机

研究了以带有Dzyaloshinski-Mariya(DM)相互作用的两比特自旋体系为工质的量子纠缠Otto热机和量子Stirling热机.两种不同热机在各自的循环过程中,通过保持其他参量不变,只有DM相互作用发生改变,从而分析热机循环中DM相互作用与热传递、做功以及效率等热力学量之间的关系.研究结果表明:DM相互作用对两种热机的基本量子热力学量都具有重要的影响,但量子Stirling热机由于回热器的使用,其循环效率会大于量子Otto纠缠热机的效率,甚至会超过Carnot效率;得到了量子Otto纠缠热机和量子Stirling热机做正功的条件.因此,在这两个纠缠体系中,热力学第二定律都依然成立.     

Ecological optimization of an irreversible harmonic oscillators Carnot heat engine

A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.     

Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.     

A thermoacoustic-Stirling heat engine: detailed study

A new type of thermoacoustic engine based on traveling waves and ideally reversible heat transfer is described. Measurements and analysis of its performance are presented. This new engine outperforms previous thermoacoustic engines, which are based on standing waves and intrinsically irreversible heat transfer, by more than 50%. At its most efficient operating point, it delivers 710 W of acoustic power to its resonator with a thermal efficiency of 0.30, corresponding to 41% of the Carnot efficiency. At its most powerful operating point, it delivers 890 W to its resonator with a thermal efficiency of 0.22. The efficiency of this engine can be degraded by two types of acoustic streaming. These are suppressed by appropriate tapering of crucial surfaces in the engine and by using additional nonlinearity to induce an opposing time-averaged pressure difference. Data are presented which show the nearly complete elimination of the streaming convective heat loads. Analysis of these and other irreversibilities show which components of the engine require further research to achieve higher efficiency. Additionally, these data show that the dynamics and acoustic power flows are well understood, but the details of the streaming suppression and associated heat convection are only qualitatively understood.     

能造出功率和效率都高的热机吗?——有限时间热力学的发展与展望

在热力学中,功率和效率是衡量热机性能的两个主要参数。根据经典热力学,可逆热机效率的上限是卡诺效率,但相应的功率为零。这是因为卡诺效率的实现依赖于时间无穷长的准静态假设。因此,如何根据实际需求,在保证热机功率前提下提高热机效率成为热力学一个重要的科学挑战问题。在20世纪上半叶应运而生的有限时间热力学,今天得到了蓬勃发展,为应对这个挑战提供了必要的科学支撑。文章主要介绍有限时间热力学的发展及现状,特别是最近对于有限时间热机功率效率约束关系及其优化问题上的研究。针对有限时间热力学循环功率—效率约束与不可逆性的关系,文章还简介最近作者关于有限时间等温过程中不可逆熵产生的理论和实验研究工作。最后展望未来有限时间热力学及有限系统非平衡物理的可能发展与应用。     

Stochastic dynamics,efficiency and sustainable power production

In the framework of stochastic thermodynamics, we give a precise expression of power dissipation in a heat engine, and study the relation between entropy and power dissipation. Using these relations, we propose a reasonable and general definition of efficiency for thermal engines in a non-equilibrium stationary state. This definition, different from Carnot efficiency, seems appropriate to the concerns of sustainable development. We show that non-zero dissipation is necessary for producing non-vanishing power. Furthermore, close to equilibrium and even in much broader situations, when power production is maximum with respect to relevant variables the power dissipation is at less equal to the power delivered to a mechanical, external system, and the corresponding “sustainable efficiency” is at most ?. From this result, we deduce a new upper bound for Carnot efficiency at maximum power. It is compared to similar, but different upper bounds obtained previously by other authors.     

以一维谐振子势阱中的单粒子为工质的量子热机性能分析

建立了以一维谐振子势阱中的单粒子为工质的量子热机模型.当势阱壁宽度和粒子的量子态缓慢改变时, 该热机类似于经典卡诺热机对外做功.假设势阱壁移动速度非常缓慢并且考虑热漏, 推导出量子热机循环的输出功率和效率等重要性能参数的一般表达式.通过优化分析, 获得了热机循环中各主要性能参数的最佳优化值和优化区间.     

Size dependence of efficiency at maximum power of heat engine

We perform a molecular dynamics computer simulation of a heat engine model to study how the engine size difference affects its performance. Upon tactically increasing the size of the model anisotropically, we determine that there exists an optimum size at which the model attains the maximum power for the shortest working period. This optimum size locates between the ballistic heat transport region and the diffusive heat transport one. We also study the size dependence of the efficiency at the maximum power. Interestingly, we find that the efficiency at the maximum power around the optimum size attains a value that has been proposed as a universal upper bound, and it even begins to exceed the bound as the size further increases. We explain this behavior of the efficiency at maximum power by using a linear response theory for the heat engine operating under a finite working period, which naturally extends the low-dissipation Carnot cycle model [M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. The theory also shows that the efficiency at the maximum power under an extreme condition may reach the Carnot efficiency in principle.     

Performance characteristics of an irreversible thermally driven Brownian microscopic heat engine

Brownian particles moving in a spatially asymmetric but periodic potential (ratchet), with an external load force and connected to an alternating hot and cold reservoir, are modeled as a microscopic heat engine, referred to as the Brownian heat engine. The heat flow via both the potential energy and the kinetic energy of the particles are considered simultaneously. The forward and backward particle currents are determined using an Arrhenius' factor. Expressions for the power output and efficiency are derived analytically. The maximum power output and efficiency are calculated. It is expounded that the Brownian heat engine is always irreversible and its efficiency cannot approach the efficiency η_C of the Carnot heat engine even in quasistatic limit. The influence of the main parameters such as the load, the barrier height of the potential, the asymmetry of the potential and the temperature ratio of the heat reservoirs on the performance of the Brownian heat engine is discussed in detail. It is found that the Brownian heat engines may be controlled to operate in different regions through variation of some parameters.     

Quantum Heat Engines with Complex Working Media,Complete Otto Cycles and Heuristics

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.     

周期性双势垒锯齿势中温差驱动的布朗热机

研究了周期性双势垒锯齿势中, 布朗粒子在外力作用下沿空间坐标方向交替地和高、低温热库接触构成的布朗热机的热力学性能. 考虑布朗粒子动能的变化以及高、 低温库之间热漏的存在, 通过数值计算分析势垒高度、势比、外力等参数对布朗热机效率的影响. 研究表明：当考虑热漏时, 布朗热机始终是不可逆的, 效率小于卡诺效率; 并且当热漏很小时, 势比的增大在一定程度上可提高布朗热机的效率; 其功率与效率之间的关系曲线为闭合线. 当不考虑热漏时, 其功率与效率之间的关系曲线为开型线, 但由于布朗粒子动能的变化引起的不可逆热流, 热机的效率依然小于卡诺效率. 关键词： 布朗热机 双势垒锯齿势 热漏 热力学性能     

Thermoelectricity without absorbing energy from the heat sources

We analyze the power output of a quantum dot machine coupled to two electronic reservoirs via thermoelectric contacts, and to two thermal reservoirs – one hot and one cold. This machine is a nanoscale analogue of a conventional thermocouple heat-engine, in which the active region being heated is unavoidably also exchanging heat with its cold environment. Heat exchange between the dot and the thermal reservoirs is treated as a capacitive coupling to electronic fluctuations in localized levels, modeled as two additional quantum dots. The resulting multiple-dot setup is described using a master equation approach. We observe an “exotic” power generation, which remains finite even when the heat absorbed from the thermal reservoirs is zero (in other words the heat coming from the hot reservoir all escapes into the cold environment). This effect can be understood in terms of a non-local effect in which the heat flow from heat source to the cold environment generates power via a mechanism which we refer to as Coulomb heat drag. It relies on the fact that there is no relaxation in the quantum dot system, so electrons within it have a non-thermal energy distribution. More poetically, one can say that we find a spatial separation of the first-law of thermodynamics (heat to work conversion) from the second-law of thermodynamics (generation of entropy). We present circumstances in which this non-thermal system can generate more power than any conventional macroscopic thermocouple (with local thermalization), even when the latter works with Carnot efficiency.     

Reprint of : Thermoelectricity without absorbing energy from the heat sources

We analyze the power output of a quantum dot machine coupled to two electronic reservoirs via thermoelectric contacts, and to two thermal reservoirs – one hot and one cold. This machine is a nanoscale analogue of a conventional thermocouple heat-engine, in which the active region being heated is unavoidably also exchanging heat with its cold environment. Heat exchange between the dot and the thermal reservoirs is treated as a capacitive coupling to electronic fluctuations in localized levels, modeled as two additional quantum dots. The resulting multiple-dot setup is described using a master equation approach. We observe an “exotic” power generation, which remains finite even when the heat absorbed from the thermal reservoirs is zero (in other words the heat coming from the hot reservoir all escapes into the cold environment). This effect can be understood in terms of a non-local effect in which the heat flow from heat source to the cold environment generates power via a mechanism which we refer to as Coulomb heat drag. It relies on the fact that there is no relaxation in the quantum dot system, so electrons within it have a non-thermal energy distribution. More poetically, one can say that we find a spatial separation of the first-law of thermodynamics (heat to work conversion) from the second-law of thermodynamics (generation of entropy). We present circumstances in which this non-thermal system can generate more power than any conventional macroscopic thermocouple (with local thermalization), even when the latter works with Carnot efficiency.     

Comparing Two Definitions of Work for a Biological Quantum Heat Engine

Systems of photosynthetic reaction centres have been modelled as heat engines, while it has also been reported that the efficiency and power of such heat engines can be enhanced by quantum interference|a trait that has attracted much interest. We compare two definitions of the work of such a photosynthetic heat engine, i.e. definition A used by Weimer et al. and B by Dorfman et al. We also introduce a coherent interaction between donor and acceptor (CIDA) to demonstrate a reversible energy transport. We show that these two definitions of work can impart contradictory results, that is, CIDA enhances the power and efficiency of the photosynthetic heat engine with definition B but not with A. Additionally, we find that both reversible and irreversible excitation-energy transport can be described with definition A, but definition B can only model irreversible transport. As a result, we conclude that definition A is more suitable for photosynthetic systems than definition B.     

一维晶格中费曼棘齿-棘爪热机

研究了一维晶格中费曼棘齿-棘爪热机模型. 用粒子的概率主方程来描述粒子在晶格中的动力学特性, 推导出热流、 功率和效率的表达式. 通过数值计算分析势垒高度、 外力和温比对热流以及热机功率和效率的影响. 研究表明: 在粒子稳态概率流为零时, 存在非零的热流从高温库流入低温库, 类似于经典不可逆卡诺模型中的热漏; 热漏的存在使得热机的效率远远小于卡诺效率, 功率与效率之间为闭合的关系曲线, 热机为不可逆热机; 对热机性能参数进行优化, 可以使热机工作在最优性能状态下.