Steepest descent path for the microcanonical ensemble-resolution of an ambiguity

The microcanonical entropy plays an essential role in the equilibrium statistical mechanics of gravitating systems. A peculiar feature of many of these systems is the existence of stable thermodynamic equilibrium configurations with negative heat capacities. Different methods have been developed for calculating the microcanonical entropy involving multivariate integrals of constraints and functional integrations. An apparent ambiguity between an approach due to Hawking and Gibbons, based on an entropy definition involving an inverse Laplace transform of the partition function, which they developed to treat quantum systems with gravity, and a different approach developed by Horwitz and Katz defining the entropy as an equal weight sum over a constant energy surface developed originally to treat Newtonian and classical GR systems is shown here to be spurious, at least at the level of quadratic fluctuations of all variables about the extremal solutions. The two approaches involve distinct contours for different orders of integration, each of which is shown to be the appropriate steepest descent path corresponding to the given order of investigation. Up to quadratic fluctuations both methods yield identical results. However, they represent different perturbation expansions for the gravitational modes of freedom with different radii of convergence. The discussion is made in terms of a particular convenient model, a system of point particles interacting via Newtonian forces, confined to a sphere, but results are quite general.     

Output power analyses of an endoreversible Carnot heat engine with irreversible heat transfer processes based on generalized heat transfer law

In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analyses method, and entransy theory to the analyses is discussed. Three numerical cases are presented. It is shown that the results obtained from the entransy theory are different from those from the entropy generation minimization, which is equivalent to the exergy analyses method. For the first case in which the application preconditions of the entropy generation minimization and entransy loss maximization are satisfied, both smaller entropy generation rate and larger entransy loss rate lead to larger output power. For the second and third cases in which the preconditions are not satisfied, the entropy generation minimization does not lead to the maximum output power, while larger entransy loss rate still leads to larger output power in the third case. For the discussed cases, the concept of entransy dissipation is not applicable for the analyses of output power.The problems in the negative comments on the entransy theory are pointed out and discussed. The related researchers are advised to focus on some new specific application cases to show if the entransy theory is the same as some other theories.     

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.     

Many-body energy localization transition in periodically driven systems

According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classical (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space.     

孤立系内热传导过程(火积)耗散的解析解

(火积)耗散与熵增均可以作为传热不可逆性的度量, 当前(火积)理论的反对者认为(火积)是不必要的. 为说明(火积)的必要性, 从有效性的角度进行了论证, 即在描述传热过程不可逆性的变化上, (火积)的严格解析解存在, 而熵的严格解析解难以得到. 本文构建了孤立系内的一维及多维热传导模型, 求解了温度及其梯度的级数型解析解, 将其代入(火积)耗散的求解式, 得到其最初的形式为一多重级数的多重积分, 交换积分与级数计算顺序, 并利用特征函数的正交性, 将(火积)耗散求解式中的积分运算求出, 并使级数的维数降低, 最终将其表示为一稳态项与一瞬态项加和的形式, 其极限与文献中的结果一致. 通过对孤立系内(火积)耗散解析解的求解可以得出: 由于热传导过程熵与(火积)的解析解求解难度不同, 在描述传热过程不可逆性变化上, (火积)更加有效; 对于孤立系内不同维数的热传导问题, 只要温度场解析解存在, (火积)耗散解析解均可以应用特征函数正交性求解得到.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

Relativistic temperature

A measurement theory for the temperature of relativistic systems is developed. The resulting operational approach is shown to be quasi-local and therefore may be applicable in general Riemannian manifolds even when there are temperature gradients which induce heat flows. The surprising feature of our analysis is that it leads to a bifurcation of the temperature concept into two distinctly different measurable quantities: one a frame invariant scalar field which a local co-moving observer would tend to identify with the local temperature and employ in the definition of entropy, the other a frame dependent, but nevertheless locally determinable quantity which governs the flow of heat and the ability to extract work. The two quantities differ by the bookkeeping methodology employed to calibrate the thermometer. A simple relationship between the two temperatures can be established if a preferred Killing vector field is available in the Riemannian manifold.     

Thermodynamic anomalies in the presence of general linear dissipation: from the free particle to the harmonic oscillator

A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat, reentrant classicality or a nonmonotonic entropy. These low-temperature phenomena are expected to be modified at very low temperatures where finite-size effects associated with the discreteness of the energy spectrum become relevant. In this paper, we explore in which form the thermodynamic anomalies visible in the specific heat and the entropy of the free damped particle appear for a damped harmonic oscillator. Since the discreteness of the oscillator’s energy spectrum is fully accounted for, the results are valid for arbitrary temperatures. As expected, they are in agreement with the third law of thermodynamics and indicate how the thermodynamic anomalies of the free damped particle can be reconciled with the third law. Particular attention is paid to the transition from the harmonic oscillator to the free particle when the limit of the oscillator frequency to zero is taken.     

A minimum entropy generation procedure for the discrete pseudo-optimization of finned-tube heat exchangers

This paper presents a novel method which can be helpful in assessing the optimal configuration of finned-tube heat exchangers. The method is an extension of the local irreversibilities method [17], and it is based on the determination on a local basis of the two components of the entropy generation rate: the one caused by viscous dissipations and the one due to thermal irreversibilities. Depending on the engineering purpose for which a technical device was designed, it can be argued that the optimal configuration will be that in which either one (or both) of these two entropy generation rates is minimized. For a heat exchanging device, it is important to minimize thermal irreversibilities, but more important is to minimize the mechanical power lost in achieving a prescribed heat-exchange performance: to this purpose, one can form a relative irreversibility index (named Bejan number here and in [17] because the original seed of this procedure can be found in [1]), and use it to assess the merit of a given configuration.In the procedure presented here, a circular, single-tube, finned heat exchanger configuration is considered: the velocity and temperature fields are computed (via a standard finite-element package, FIDAP) for a realistic value of the Reynolds number and for a variety of geometric configurations (various fin external diameters and fin spacing); then, the entropy generation rate is calculated from the flowfield, and is examined both at a local level, to detect possible bad design spots (ie, locations which correspond to abnormally high entropy generation rates, which could be cured by design improvements), and at an overall (integral) level, to assess the entropic performance of the heat exchanger. Optimal curves are given, and the optimal spacing of fins is determined using alternatively the entropy generation rate and the total heat transfer rate as objective functions: different optima arise, and the differences as well as the similarities are discussed in detail.     

Entropy corrections for Schwarzschild black holes

Recently it is shown that the Bekenstein–Hawking entropy for black holes receives logarithmic corrections due to thermodynamic fluctuations. Schwarzschild black hole which possesses a negative specific heat is thermodynamically unstable, so the entropy corrections cannot be obtained directly. In this Letter, Schwarzschild black hole will be put in the center of a spherical cavity of finite radius to achieve equilibrium with surroundings, so that a thermodynamically stable solution is obtained based on a uniformly spaced area spectrum approach. Our conclusion show that there are two correction terms for Schwarzschild black holes. The sign of the second correction term depends on the size of the cavity.     

Effects of Gaussian thermal fluctuations on the thermodynamic of microtubules in Landau-Ginzburg-Wilson model

This paper investigates microtubule thermodynamic properties dependence on gaussian thermal fluctuations using the Landau-Ginzburg-Wilson model. After solving the self-consistent equation for thermal fluctuations, we observed its increasing behavior as a function of temperature for different dimensionality 1, 2 and 3. Thermodynamic properties such as Shannon entropy, thermodynamic entropy, heat capacity and chemical potential have been computed. We found out that under thermal fluctuations, heat capacity and chemical potential exhibit negative values that can refer to the coexistence of first and second order phase transitions during MT dynamic instability. We also found that thermodynamic properties are highly affected at low temperatures. Moreover, thermodynamic entropy locally displays the conversion of the heat into work through the negentropy. We analyzed the behavior of the polarization according to fluctuations and found that thermal fluctuations modulate the polarization and depolarization of tubulin dimers which is very important in information processing in microtubules.     

Nonequilibrium thermodynamics of stochastic systems with odd and even variables

The total entropy production of stochastic systems can be divided into three quantities. The first corresponds to the excess heat, while the second two comprise the housekeeping heat. We denote these two components the transient and generalized housekeeping heat and we obtain an integral fluctuation theorem for the latter, valid for all Markovian stochastic dynamics. A previously reported formalism is obtained when the stationary probability distribution is symmetric for all variables that are odd under time reversal, which restricts consideration of directional variables such as velocity.     

A quantum field theory of the liquid-glass transition in multi-component liquids

An established unified theory of the liquid-glass transition in one-component liquids is extended to multi-component liquids. The universal features such as the Kauzmann paradox, the Vogel-Tamman-Fulcher (VTF) law on the relaxation times and the transport coefficients, the jump of the specific heat at the glass transition temperature and the Boson peaks are elucidated. The Kauzmann entropy in a form of a Curie law with a negative sign comes from the mixing between the sound and the intra-band fluctuation entropies, where the critical temperature corresponds to the sound instability temperature at a reciprocal particle distance. The VTF law is constructed from the Einstein relation on entropy and probability so that the Kauzmann entropy is included as a normal form in exponent of the VTF law. The Kauzmann entropy explains the Kauzmann paradox and the jump of the specific heat so that the universal features of the glass transition are elucidated consistently.     

Verification of numerical simulation method for entropy generation of radiation heat transfer in semitransparent medium

The numerical simulation method of radiative entropy generation in participating media presented by Caldas and Semiao [Entropy generation through radiative transfer in participating media: analysis and numerical computation. JQSRT 2005;96:423-37] is extended to analyze the radiative entropy generation in the enclosures filled with semitransparent media. A discrete ordinates method is used to solve radiative transfer equation and radiative entropy generation. Two different examples are employed to verify the numerical simulation method of radiative entropy generation in the enclosure. Numerical results of dimensionless radiative entropy generation of enclosure are identical to that of entire thermodynamics analysis for the enclosure system. This numerical simulation method can be used in the entropy generation analysis of high-temperature systems such as boilers and furnaces, in which radiation is the dominant mode of heat transfer.     

Thermodynamic product formula for a Taub–NUT black hole

We derive various important thermodynamic relations of the inner and outer horizons in the background of the Taub–NUT (Newman–Unti–Tamburino) black hole in four-dimensional Lorentzian geometry. We compare these properties with the properties of the Reissner–Nordström black hole. We compute the area product, area sum, area subtraction, and area division of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From the area bound, we derive an entropy bound and an irreducible mass bound for both horizons. We further study the stability of such black holes by computing the specific heat for both horizons. It is shown that due to the negative specific heat, the black hole is thermodynamically unstable. All these calculations might be helpful in understanding the nature of the black hole entropy (both interior and exterior) at the microscopic level.     

Microcanonical analyses of peptide aggregation processes

We propose the use of microcanonical analyses for numerical studies of peptide aggregation transitions. Performing multicanonical Monte Carlo simulations of a simple hydrophobic-polar continuum model for interacting heteropolymers of finite length, we find that the microcanonical entropy behaves convex in the transition region, leading to a negative microcanonical specific heat. As this effect is also seen in first-order-like transitions of other finite systems, our results provide clear evidence for recent hints that the characterization of phase separation in first-order-like transitions of finite systems profits from this microcanonical view.     

Stability analysis of the classical ideal gas in nonextensive statistics and the negative specific heat

We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use this theory to understand the phenomena of negative specific heat in the nonextensive gas. The stability analysis is made on the basis of the second variation of Tsallis entropy. It is shown that the system is thermodynamically unstable if the nonextensive parameter is q>5/3, which is exactly equivalent to the condition of appearance of the negative specific heat.     

Energy and Entropy Analyses of a Pilot-Scale Dual Heating HDH Desalination System

This study focuses on energy and entropy analysis to theoretically investigate the performance of a pilot scale dual heated humidification-dehumidification (HDH) desalination system. Two cases of HDH systems are considered in the analysis. The first case is a dual heated (DH) cycle consisting of 1.59 kW air heater and 1.42 kW water heater with a heat rate ratio of 0.89 (CAOW-DH-I). Whereas the second case is a dual heated HDH cycle comprising of 1.59 kW air heater and 2.82 kW water heater with a heat rate ratio of 1.77 (CAOW-DH-II). As a first step, mathematical code was developed based on heat and mass transfer and entropy generation within the major components of the system. The code was validated against the experimental data obtained from a pilot scale HDH system and was found to be in a good agreement with the experimental results. Theoretical results revealed that there is an optimal mass flowrate ratio at which GOR is maximized, and entropy generation is minimized. Furthermore, the degree of irreversibility within the humidifier component is low and approaches zero, while the specific entropy generation within other components are relatively high and are of the same order of magnitude. Entropy analysis also showed that the dual heated system with heat rate ratio greater than unity is better than the one with heat rate ratio less than unity.