Second law of thermodynamics with discrete quantum feedback control

A new thermodynamic inequality is derived which leads to the maximum work that can be extracted from multi-heat-baths with the assistance of discrete quantum feedback control. The maximum work is determined by the free-energy difference and a generalized mutual information content between the thermodynamic system and the feedback controller. This maximum work can exceed that in conventional thermodynamics and, in the case of a heat cycle with two heat baths, the heat efficiency can be greater than that of the Carnot cycle. The consistency of our results with the second law of thermodynamics is ensured by the fact that work is needed for information processing of the feedback controller.     

Efficiency of reverse cycles

It is demonstrated that the generally accepted treatment of the second law of thermodynamics is incorrect when the statement of the maximum limiting efficiency of the forward Carnot cycle is applied to the reverse cycles. An analysis of reversible cycles compared with the Carnot cycle shows that the reverse Carnot cycle has the lowest efficiency of all reverse cycles. A new characteristic is proposed — the thermal efficiency of reverse cycles, and a generalized theorem is put forward for the additivity of the thermal efficiencies of the forward and reverse cycles. A formulation of the second law of thermodynamics is suggested from the point of view of the efficiency of reverse cycles. Zh. Tekh. Fiz. 69, 11–14 (June 1999)     

Can Quantum Correlations Lead to Violation of the Second Law of Thermodynamics?

Quantum entanglement can cause the efficiency of a heat engine to be greater than the efficiency of the Carnot cycle. However, this does not mean a violation of the second law of thermodynamics, since there is no local equilibrium for pure quantum states, and, in the absence of local equilibrium, thermodynamics cannot be formulated correctly. Von Neumann entropy is not a thermodynamic quantity, although it can characterize the ordering of a system. In the case of the entanglement of the particles of the system with the environment, the concept of an isolated system should be refined. In any case, quantum correlations cannot lead to a violation of the second law of thermodynamics in any of its formulations. This article is devoted to a technical discussion of the expected results on the role of quantum entanglement in thermodynamics.     

正、反向两源热力循环有限时间热力学性能优化的研究进展

有限时间热力学所得结果具有普适性,其研究结果已成为热物理学的一个重要基础.许多学者利用有限时间热力学方法对单级和多级正、反向两热源热力循环最优性能和最优构型进行了大量研究,获得了一些比经典热力学对于工程设计和优化更具有实际指导意义的新结论.综述了利用有限时间热力学理论对不同传热规律下单级和多级正、反向两热源热力循环最优性能和最优构型研究的最新进展,包括不同传热规律下内可逆和不可逆卡诺热机、制冷机和热泵循环的最优性能研究进展,两热源热机、制冷和热泵循环最优构型及多级复杂热力系统最优构型研究进展.     

Charged torus-like black holes as heat engines

We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines. In the extended phase space, by interpreting the cosmological constant as the thermodynamic pressure, we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state. Then, we calculate the efficiency of the heat engine in the Carnot cycle as well as the rectangular cycle,and investigate how the efficiency changes with respect to volume. In addition, to avoid a negative temperature, we emphasize that the charge of this black hole cannot be arbitrary. Last,we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.     

The Second Law of Thermodynamics in a Quantum Heat Engine Model

The second law of thermodynamics has been proven by many facts in classical world. Is there any new property of it in quantum world? In this paper, we calculate the change of entropy in T.D. Kieu's model for quantum heat engine (QHE) and prove the broad validity of the second law of thermodynamics. It is shown that the entropy of the quantum heat engine neither decreases in a whole cycle, nor decreases in either stage of the cycle. The second law of thermodynamics still holds in this QHE model. Moreover, although the modified quantum heat engine is capable of extracting more work, its efficiency does not improve at all. It is neither beyond the efficiency of T.D. Kieu's initial model, nor greater than the reversible Carnot efficiency.     

Carnot cycles in general relativity

Classical thermodynamics has been developed with the assumption that, either no gravitational fields are present in the thermodynamic systems, or that the fields act on the Newtonian mass of the systems only and not on any other kind of internal energy like heat. In order to find the exact thermodynamic relations for systems with gravitational fields, the wellknown Carnot cycles are used, taking into account the action of gravitation. The gravitation is described by general relativity. The Carnot efficiency is calculated in the case of stationary fields. Temperature for general relativistic systems can be defined with the help of Kelvin's principle analogously to classical thermodynamics, and the Carnot efficiency can then be expressed with temperatures instead of heat energies. In the case of strong gravitational fields, the Carnot efficiency can become equal to one even if the temperatures are both different from zero. Thermodynamic equilibrium can be expressed by using the Carnot efficiency, and it can be proved that for equilibrium the Tolman relation = constantholds quite generally for systems with stationary gravitational fields.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.For 1969–71 on leave of absence at the Center for Relativity Theory, University of Texas at Austin, Austin, Texas, as a Faculty Associate supported by the National Science Foundation (Grant No. GU-1598).     

热力学第二定律理论体系的讨论

热力学第二定律原有的两个理论体系都有明显的不足之处,为此,综全各种方法的优点,利用我们提出的简单物质可逆补热循环以及微分方程基本理论,简单明确地直接由热力学第二定律的开尔文表述推导克劳修斯等式、不等式,在推导过程中自然地引出绝对温度,得到热力学熵和增加原理,从而建立起热力学第二定律的新理论体系。     

The second law of thermodynamics revisited I. The absolute zero of potential and the general expression for the efficiency of universal reversible cycle

The fundamental equation of thermodynamics expresses the internal energy of a system as a function of all the extensive parameters of the system. The differential form of this equation is referred to as the Gibbs equation. We have integrated this equation and have used it to derive an expression characterising the efficiency of a system for any kind of cyclical process by which work is produced. This system has access to two reservoirs at low and high thermodynamics potential respectively. It is claimed that all thermodynamic potentials (temprature, chemical potential, hydrostatic pressure, electric potential, etc) can have an absolute value of zero which we defined as the value of the potential in the lower reservoir when the efficiency of the cycle is 1. It is also shown that the classical Carnot machine, in which heat is converted into mechanical work, is an example of the general expression.     

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.     

Origin of negative temperatures in systems interacting with external fields

The controversial existence of negative temperatures has stirred interesting debates that have reached the foundations of thermodynamics, including questions on the second law, the Carnot efficiency and the statistical definition of entropy. Here we show that for systems interacting with an external field, negative temperatures may arise when the interaction energy with the field is treated as a form of internal energy. We discuss how negative temperatures are avoided when using a thermodynamic formalism that accounts for the intensive and extensive variables associated to the external field. We use the paramagnetic system and a perfect gas in a gravitational field to illustrate these ideas. Considerations about the isothermal and adiabatic work done by the field or the system also shed light on the inconsistency of super-Carnot efficiencies.     

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.     

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.     

Entangled quantum heat engines based on two two-spin systems with Dzyaloshinski-Moriya anisotropic antisymmetric interaction

We construct an entangled quantum heat engine (EQHE) based on two two-spin systems with Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction. By applying the explanations of heat transferred and work performed at the quantum level in Kieu’s work [Phys. Rev. Lett. 93, 140403 (2004)], the basic thermodynamic quantities, i.e., heat transferred, net work done in a cycle and efficiency of EQHE are investigated in terms of DM interaction and concurrence. The validity of the second law of thermodynamics is confirmed in the entangled system. It is found that there is a same efficiency for both antiferromagnetic and ferromagnetic cases, and the efficiency can be controlled in two manners: (1) only by spin-spin interaction J and DM interaction D; (2) only by the temperature T and concurrence C. In order to obtain a positive net work, we need not entangle all qubits in two two-spin systems and we only require the entanglement between qubits in a two-spin system not be zero. As the ratio of entanglement between qubits in two two-spin systems increases, the efficiency will approach infinitely the classical Carnot one. An interesting phenomenon is an abrupt transition of the efficiency when the entanglements between qubits in two two-spin systems are equal.     

f(R) Black Holes as Heat Engines

With the cosmological constant considered as a thermodynamic variable in the extended phase space, it is natural to study the thermodynamic cycles of the black hole, which is conjectured to be performed using renormalization group flow. We first investigate the thermodynamic cycles of a 4-dimensional asymptotically AdS f(R) black hole. Then we study the thermodynamic cycles of higher dimensional asymptotically AdS f(R) black holes. It is found that when ΔV ? ΔP, the efficiency of isobar-isochore cycles running between high temperature T_H and low temperature T_C will increase to its maximum value, which is exactly the Carnot cycles’ efficiency both in 4-dimensional and in higher dimensional cases. We speculate that this property is universal for AdS black holes, if there is no phase transition in the thermodynamic cycle. This result may deepen our understanding of the thermodynamics of the AdS black holes.     

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.     

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.     

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。     

关于吸收式碳捕集热力学机制的探索

热再生吸收式碳捕集的传统认识难以揭示其热力学机制,一种新的认识是"热-化学能"转换中存在中间能量形式。本文从热力学碳泵概念出发,对吸收式碳捕集理想系统进行了解耦,其可视为"热机-碳泵"的热力学组合,探索了极限效率的表达,并采用第二定律效率作为评价参数对已有中试试验系统进行了性能水平探索。结果表明,理想循环性能系数仅取决于热源汇温度、碳源汇浓度;中试系统第二定律效率普遍低于20%。本文探索了热驱动的吸收式碳捕集热力学机制,为新型吸收剂设计提供了新思路。     

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