Extracting Work Optimally with Imprecise Measurements

Measurement and feedback allows for an external agent to extract work from a system in contact with a single thermal bath. The maximum amount of work that can be extracted in a single measurement and the corresponding feedback loop is given by the information that is acquired via the measurement, a result that manifests the close relation between information theory and stochastic thermodynamics. In this paper, we show how to reversibly confine a Brownian particle in an optical tweezer potential and then extract the corresponding increase of the free energy as work. By repeatedly tracking the position of the particle and modifying the potential accordingly, we can extract work optimally, even with a high degree of inaccuracy in the measurements.     

Optimisation thermodynamique en temps fini du moteur de Stirling endo- et exo-irréversible

Finite-time thermodynamics optimisation of an endo- exo-irreversible Stirling Motor. This work deals with the finite time thermodynamic optimization of a Stirling engine. An endo- and exo-irreversible cycle is considered. The internal irreversibilities are due to the internal conductance of the plant and to the non-adiabatic regenerator. Also, the general irreversibilities of the non-quasistatic cycle are taken into account. The external irreversibilities are due to the linear interactions between the heat sources and the working fluids at finite temperature gaps.A sensitivity analysis was performed in order to optimize the operation conditions leading to maximum power output. The results obtained are in good agreement with the experimental data.     

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.     

Generalization of the second law for a nonequilibrium initial state

We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also tells us the maximum work that may be gained from a nonequilibrium initial state. The generalized second law also gives a fundamental relation between work and information. It is valid even for a small Hamiltonian system not in contact with a heat reservoir but with an effective temperature determined by the isentropic condition. Our relation can be tested in the Szilard engine, which will be realized in the laboratory.     

以范德瓦耳斯气体为工质的3种热机循环效率

利用热力学的普遍理论推导了范德瓦尔斯气体热力学函数的表达式,再求出绝热过程和3种等值过程中功和热量的表达式.在此基础上,研究了斯特林循环、奥拓循环和狄塞尔循环的功和效率,并计算和分析了3种循环效率随各种参量变化的关系.     

(火积)理论在热功转换过程中的应用探讨

分析和讨论了(火积)理论在热功转换过程的应用及其局限性.对Carnot循环的分析表明,Carnot循环中系统的(火积)是平衡的,但(火积)和熵之间不存在dG=T2dS这样的联系.对于一般热力学过程,分析表明,在热量传递到内可逆循环中间接对外做功时,现有的(火积)理论可用于系统的分析.讨论了热功转换过程分析中(火积)理论与熵理论的不同.分析表明,两个理论的分析角度及优化输出功的前提条件是不同的.熵产从可用能损失的角度分析热功转换过程,而(火积)理论则从热量势能消耗的角度.当输入系统的可用能给定或者输入系统的热量及热量进、出系统的热力学力给定时,熵产最小化对应于输出功最大;对于(火积)理论,则当输入系统的热量及热量进、出系统的温度给定时,最大(火积)损失对应于最大输出功.同时,它们各自均有局限性.当相应的前提条件不满足时,最大(火积)损失或最小熵产可能不与最大输出功相对应.     

理想气体热力学过程吸放热情况的图像判断法

如何简便地判断一个热力学过程的吸放热情况,对于了解此热力学过程是至关重要的．传统的方法是借助热力学第一定律,通过计算该热力学过程中的热学三量（功、热量和内能）来确定．文章通过分析简单热力学过程中的热容,得出：从绝热线上一点出发的微过程,过程曲线在绝热线下方,为放热过程;反之,为吸热过程．进一步,文章指出对于一些复杂的热力学过程,除使用传统的比较功大小的方法外,还可以利用热力学过程的末态相对等温线的位置而简单得出其吸放热情况。     

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.     

Onsager coefficients of a Brownian Carnot cycle

We study a Brownian Carnot cycle introduced by Schmiedl and Seifert [Europhys. Lett. 81, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we can determine thermodynamic forces and fluxes of the cycle and calculate the Onsager coefficients for general protocols, that is, arbitrary schedules to change the potential confining the Brownian particle. We show that these Onsager coefficients contain the information of the protocol shape and they satisfy the tight-coupling condition irrespective of whatever protocol shape we choose. These properties may give an explanation why the Curzon-Ahlborn efficiency often appears in the finite-time heat engines.     

影响热虹吸管运行性能的参数分析

依据热力学第二定律,在分析热管运行过程的基础上,建立了热管工质循环过程的T-S熵分析模型,对热管稳态运行时的几何参数和工质流体热物性参数进行分析,推导得出了热管设计和成功运行的基本条件,热管的结构参数组必须大于工质的热物性参数和封装材料组,二者相容才能建立热管的热力循环。用试验结果验证了此结论。所推导的方程对于一定结构的热管提供了一个设计和运行的指导准则,并且与传热率无关,不管热流多大热管结构参数必须和材料相容。     

多孔介质(PM)发动机理想循环热力学分析

本文论述了基于多孔介质燃烧技术的超绝热发动机的原理及其工作过程,建立了PM发动机的热力学模型,对 PM发动机内的PM回热循环进行热力学分析,列出了循环参数如压缩比、预胀比、预压比等对发动机效率、循环功的影响,确定了PM回热循环的两种极限状态。将PM回热循环与发动机的Otto循环、Diesel循环进行比较,结果表明: PM回热循环在保证效率的同时,可以大幅度提高循环功。     

Thermodynamic model for feedback control of systems with uncertain macroscopic states

Thermodynamics of feedback control processes, including the minimum work consumption of measurement, work extraction, and erasure processes of thermodynamic small systems have been investigated by researchers. We take systems with uncertain macroscopic states as the study object and study the feedback control processes of nonequilibrium macroscopic systems considering both the information entropy of microscopic states and macroscopic states. First we consider a system set that consists of systems with several macroscopic states and discuss the relations among the average information entropy of the system set, the thermodynamic entropy of the systems and the information entropy of macroscopic states of the systems. Then, we derive the expression of the average maximum net work obtained through feedback control, which relates to the free energy of the systems and the minimum work consumption of the measurement and erasure processes.     

Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr²ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr²ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’, exclusively to negative Gibbs energy (−G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates.     

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.     

Fluctuation theorem for entropy production at strong coupling

Fluctuation theorems have been applied successfully to any system away from thermal equilibrium, which are helpful for understanding the thermodynamic state evolution. We investigate fluctuation theorems for strong coupling between a system and its reservoir, by path-dependent definition of work and heat satisfying the first law of thermodynamics. We present the fluctuation theorems for two kinds of entropy productions. One is the informational entropy production, which is always non-negative and can be employed in either strong or weak coupling systems. The other is the thermodynamic entropy production, which differs from the informational entropy production at strong coupling by the effects regarding the reservoir. We find that, it is the negative work on the reservoir, rather than the nonequilibrium of the thermal reservoir,which invalidates the thermodynamic entropy production at strong coupling. Our results indicate that the effects from the reservoir are essential to understanding thermodynamic processes at strong coupling.     

Generalization of the second law for a transition between nonequilibrium states

The maximum work formulation of the second law of thermodynamics is generalized for a transition between nonequilibrium states. The relative entropy, the Kullback-Leibler divergence between the nonequilibrium states and the canonical distribution, determines the maximum ability to work. The difference between the final and the initial relative entropies with an effective temperature gives the maximum dissipative work for both adiabatic and isothermal processes. Our formulation reduces to both the Vaikuntanathan-Jarzynski relation and the nonequilibrium Clausius relation in certain situations. By applying our formulation to a heat engine the Carnot cycle is generalized to a circulation among nonequilibrium states.     

Nonequilibrium work relations: foundations and applications

When a macroscopic system in contact with a heat reservoir is driven away from equilibrium, the second law of thermodynamics places a strict bound on the amount of work performed on the system. With a microscopic system the situation is more subtle, as thermal fluctuations give rise to a statistical distribution of work values. In recent years it has been realized that such distributions encode surprisingly more information than one might expect from traditional thermodynamic arguments. I will discuss a number of exact results that relate equilibrium properties of the system, in particular free energy differences, to the fluctuations in the work performed during such a nonequilibrium process. I will describe the theoretical foundations of these relations, connections with irreversibility and the second law of thermodynamics, and potential experimental and computational applications.     

The Natural Philosophy of Economic Information: Autonomous Agents and Physiosemiosis

Information is a core concept in modern economics, yet its definition and empirical specification is elusive. One reason is the intellectual grip of the Shannon paradigm which marginalizes semantic information. However, a precise concept of economic information must be based on a theory of semantics, since what counts economically is the meaning, function and use of information. This paper introduces a new principled approach to information that adopts the paradigm of biosemiotics, rooted in the philosophy of Charles S. Peirce and builds on recent developments of the thermodynamics of information. Information processing by autonomous agents, defined as autopoietic heat engines, is conceived as physiosemiosis operating according to fundamental thermodynamic principles of information processing, as elucidated in recent work by Kolchinsky and Wolpert (KW). I plug the KW approach into a basic conceptual model of physiosemiosis and present an evolutionary interpretation. This approach has far-reaching implications for economics, such as suggesting an evolutionary view of the economic agent, choice and behavior, which is informed by applications of statistical thermodynamics on the brain.     

Nonequilibrium free energy and information flow of a double quantum-dot system with Coulomb coupling

We build a double quantum-dot system with Coulomb coupling and aim at studying connections among the entropy production, free energy, and information flow. By utilizing concepts in stochastic thermodynamics and graph theory analysis, Clausius and nonequilibrium free energy inequalities are built to interpret local second law of thermodynamics for subsystems. A fundamental set of cycle fluxes and affinities is identified to decompose two inequalities by using Schnakenberg's network theory. Results show that the thermodynamic irreversibility has energy-related and information-related contributions. A global cycle associated with the feedback-induced information flow would pump electrons against the bias voltage, which implements a Maxwell demon.