Resolution of a Classical Gravitational Second-Law Paradox

Sheehan and coworkers have claimed [D. P. Sheehan et al., Found. Phys. 30, 1227 (2000); 32, 441 (2002); D. P. Sheehan, in Quantum Limits to the Second Law, AIP Conference Proceedings 643 (American Institute of Physics, Melville, NY, 2002), p. 391] that a dilute gas trapped between an external shell and a gravitator can support a steady state in which energy flux by particles in one direction is balanced by energy flux by radiation in the opposite direction, and in which work can be extracted from an isothermal heat reservoir, thereby violating the second law of thermodynamics. In this paper, we identify a fundamental error in their simulation and analysis of their model system that vitiates their conclusions. We analyze a simpler, exactly soluble, three-dimensional model of a very dilute gas in a gravitational field between two thermal reservoirs, and show that their conclusions are not supported for the simple model. We show that their method of simulation, when applied to either the simple model or their more complex model under simpler conditions where the answers are known, leads to unphysical results. We also show that, when appropriate sampling is done, their model gives results in accord with the second law and detailed balance.     

Experimental Test of a Thermodynamic Paradox

In 2000, a simple, foundational thermodynamic paradox was proposed: a sealed blackbody cavity contains a diatomic gas and a radiometer whose apposing vane surfaces dissociate and recombine the gas to different degrees (A $_{2} \rightleftharpoons $ 2A). As a result of differing desorption rates for A and A $_{2}$ , there arise between the vane faces permanent pressure and temperature differences, either of which can be harnessed to perform work, in apparent conflict with the second law of thermodynamics. Here we report on the first experimental realization of this paradox, involving the dissociation of low-pressure hydrogen gas on high-temperature refractory metals (tungsten and rhenium) under blackbody cavity conditions. The results, corroborated by other laboratory studies and supported by theory, confirm the paradoxical temperature difference and point to physics beyond the traditional understanding of the second law.     

Information conservation, entropy increase and statistical irreversibility for an isolated system

We consider statistical irreversibility and its compatibility with reversible dynamics. The role played by the observation is analyzed in detail. It makes our previous proof for the second law of thermodynamics clearer. On this basis, we emphasize the importance and wide applicability of the second law of thermodynamics. A new form of physics with this law substituted by the principle of information conservation is suggested. By the way, we also solve the paradox of Schrödinger cat, and show that the universe will not go to the so-called heat death spontaneously.     

Maxwell’s demon and the management of ignorance in stochastic thermodynamics

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.     

Laser spectroscopy of nuclear reaction products: recent results and future prospects

Laser spectroscopic observations of nuclear reaction products produced with intensities of less than 10⁴ atoms/second are now possible with several different methods. We describe the recoil into gas method which has recently been successful. This method is not Dopplerfree, but can give reasonable spectra if the resolution requirements of the spectra are not too high. It has the great advantage that it very efficiently uses the atoms, and spectra have been observed with primary production rates of less than 10³ atoms/sec. Our recent work has concentrated on developing the recoil into gas method for the refractory element Hf. In order that the atoms could be cycled to produce many fluorescence photons, nitrogen and hydrogen impurity gases were added to the argon buffer gas to quench metastable levels to the ground state. In this way spectra could be obtained with fluxes of 10⁴ atoms/second. Future prospects for trapping radioactive atoms in a magneto-optic trap will be discussed.     

Interferometrische Bestimmung der Gastemperatur in der Stickstoffniederdruckentladung

A Michelson-interferometer in combination with a He-Ne-laser was used to determine the gas temperature in a nitrogen low pressure gas discharge. With this method the radial temperature profile could be measured to about 96% of the tube radius. Moreover rotational temperatures were measured with a 2 m-grating spectrograph from the spectrum of N₂- and N₂⁺-bands. In the range from 4 to 10 torr and 25 to 100 mA gas temperatures between 460 and 890 K were measured with the belonging rotational temperature from 620 to 1170 K. At pressures below 10 torr a difference of the rotational temperatures from the first negative and the second positive system was found. A qualitative consideration on the mechanism of the radial heat conductivity in the positive column was added.     

Thermal and efficiency analysis of the CO2 laser cutting process

In CO₂ laser gas-assisted cutting process, modeling of the interaction mechanism is important. Consequently, the present study treats the complete problem of the interaction of the melting surface with the boundary layer and describes the behavior of the melting layer. In the analysis, gas–liquid interface parameters are developed and relationships between the parameters influencing the cutting action are identified theoretically. To achieve this, effects of momentum and gas–liquid interface shear stress, due to the assisting gas jet, are considered. The approximate magnitude of the heat absorbed is estimated and melting layer thickness is predicted. An experiment is carried out and the theoretical predictions are compared with the experimental findings. First and second law efficiencies of the cutting process are predicted, which may, then, be used to improve the process. It is found that the assisting jet velocity increases the first and second law efficiencies of the CO₂ laser cutting process.     

Entropy Generation Analysis of the Flow Boiling in Microgravity Field

Entropy generation analysis of the flow boiling in microgravity field is conducted in this paper. A new entropy generation model based on the flow pattern and the phase change process is developed in this study. The velocity ranges from 1 m/s to 4 m/s, and the heat flux ranges from 10,000 W/m² to 50,000 W/m², so as to investigate their influence on irreversibility during flow boiling in the tunnel. A phase–change model verified by the Stefan problem is employed in this paper to simulate the phase–change process in boiling. The numerical simulations are carried out on ANSYS-FLUENT. The entropy generation produced by the heat transfer, viscous dissipation, turbulent dissipation, and phase change are observed at different working conditions. Moreover, the Be number and a new evaluation number, E_P, are introduced in this paper to investigate the performance of the boiling phenomenon. The following conclusions are obtained: (1) a high local entropy generation will be obtained when only heat conduction in vapor occurs near the hot wall, whereas a low local entropy generation will be obtained when heat conduction in water or evaporation occurs near the hot wall; (2) the entropy generation and the Be number are positively correlated with the heat flux, which indicates that the heat transfer entropy generation becomes the major contributor of the total entropy generation with the increase of the heat flux; (3) the transition of the boiling status shows different trends at different velocities, which affects the irreversibility in the tunnel; (4) the critical heat flux (CHF) is the optimal choice under the comprehensive consideration of the first law and the second law of the thermodynamics.     

Onsager-Machlup Theory for Nonequilibrium Steady States and Fluctuation Theorems

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integral for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit. PACS numbers: 05.70.Ln, 05.40.-a, 05.10.Gg.     

Equation of State of 20Ne gas in the temperature-range 27–36 K

The many-body phase shifts for ²⁰Ne gas are calculated for low number densities in the temperature-range 27–36?K, using the Galitskii-Migdal-Feynman formalism. These phase shifts are inserted in the Beth-Uhlenbeck formula to determine the quantum second virial coefficient. This is compared to the classical coefficient as well as to the experimental values and other theoretical results. It is used to investigate the pressure-volume-temperature behavior of the gas and to compute other thermodynamic properties – the Helmholtz free energy, total internal energy, entropy, and specific heat capacity – for a number density of 1×?10²⁷ atoms/m³. Our results show that, in cooling and compressing the system, vapor-liquid condensation always occurs.     

Heat conduction paradox involving second-sound propagation in moving media

In this Letter, we revisit the Maxwell-Cattaneo law of finite-speed heat conduction. We point out that the usual form of this law, which involves a partial time derivative, leads to a paradoxical result if the body is in motion. We then show that by using the material derivative of the thermal flux, in lieu of the local one, the paradox is completely resolved. Specifically, that using the material derivative yields a constitutive relation that is Galilean invariant. Finally, we show that under this invariant reformulation, the system of governing equations, while still hyperbolic, cannot be reduced to a single transport equation in the multidimensional case.     

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。     

Phase Space Portraits of an Unresolved Gravitational Maxwell Demon

In 1885, during initial discussions of J. C. Maxwell's celebrated thermodynamic demon, Whiting ⁽¹⁾ observed that the demon-like velocity selection of molecules can occur in a gravitationally bound gas. Recently, a gravitational Maxwell demon has been proposed which makes use of this observation [D. P. Sheehan, J. Glick, and J. D. Means, Found. Phys. 30, 1227 (2000)]. Here we report on numerical simulations that detail its microscopic phase space structure. Results verify the previously hypothesized mechanism of its paradoxical behavior. This system appears to be the only example of a fully classical mechanical Maxwell demon that has not been resolved in favor of the second law of thermodynamics.     

Emergence of the Second Law out of Reversible Dynamics

If one demystifies entropy the second law of thermodynamics comes out as an emergent property entirely based on the simple dynamic mechanical laws that govern the motion and energies of system parts on a micro-scale. The emergence of the second law is illustrated in this paper through the development of a new, very simple and highly efficient technique to compare time-averaged energies in isolated conservative linear large scale dynamical systems. Entropy is replaced by a notion that is much more transparent and more or less dual called ectropy. Ectropy has been introduced before but we further modify the notion of ectropy such that the unit in which it is expressed becomes the unit of energy. The second law of thermodynamics in terms of ectropy states that ectropy decreases with time on a large enough time-scale and has an absolute minimum equal to zero. Zero ectropy corresponds to energy equipartition. Basically we show that by enlarging the dimension of an isolated conservative linear dynamical system and the dimension of the system parts over which we consider time-averaged energy partition, the tendency towards equipartition increases while equipartition is achieved in the limit. This illustrates that the second law is an emergent property of these systems. Finally from our large scale linear dynamic model we clarify Loschmidt’s paradox concerning the irreversible behavior of ectropy obtained from the reversible dynamic laws that govern motion and energy at the micro-scale.     

The evolution of free turbulent spherical gas flames and the generalized Kolmogorov-Obukhov laws

A scenario of self-turbulization and limiting (experimentally observed) laws of accelerated expansion of a free turbulent spherical flame in a preliminarily mixed fuel gas mixture are described. The limiting self-similar law of the growth of a completely turbulized spherical front R ～ 〈?〉^1/2 t ^3/2 was shown to correspond to the generalized Kolmogorov-Obukhov law for a locally isotropic velocity field in a spherical turbulent medium with an immobile center of gravity at a constant rate of internal heat release per 1 kg of the mixture 〈?〉 (in m²/s³). The asymptotic dependences of the kinematic (space-time) characteristics of the evolution of a turbulent macroelement growing according to the Kolmogorov-Obukhov laws on the Reynolds and Peclet numbers obtained from the visible radius R, the rate of its propagation R′, and laminar viscosity (v) and thermal diffusivity (χ) coefficients of the initial mixture were obtained in the criterional form. It was shown that, irrespective of the direction of cloud growth under study (horizontal impurity diffusion in the atmosphere and ocean or an isotropic spherical flame) and the physical nature and value of internal heat release 〈?〉 in this direction (viscous dissipation of the kinetic energy of turbulent vortices in the first case or energy release in combustion in the second), the kinematic parameters of the growth of turbulent macroformations were described by these generalized laws.     

锑化铟的热处理

本文叙述N型InSb单晶和含有大晶粒的双晶样品(n～1.23×10¹⁴—2.40×10¹⁵cm^-3,μ_e～5.15×10⁵cm²/V·sec—2.10×10⁵cm²/V·sec),在500℃下、不同气氛中进行热处理产生受主,引起热转换,而整块地变为P型样品,当继续热处理使温度达到熔点以上时,这种P型样品中的热受主消失了,而转变回到原来的N型样品;若把这种N型样品再在500℃下进行热处理,则它又整块地变为P型样品。我们对这一新发现的过程进行了一些研究,发现这种现象与材料的不同制备条件和热处理时的环境气氛不同有关,并对不同气氛下的循环热转换过程和熔化效应作了论述。在500℃下进行热处理所引起的热受主浓度与热处理时间的关系中,发现在热处理起始的一段时间内,热受主形成速率较大;随着热处理时间的增加,热受主浓度达到一个饱和值;若再加长热处理时间,则热受主浓度开始下降,这现象与硅的热处理现象相似。根据实验得到的新结果进行分析,认为这种热处理现象不象是外来因素的影响所引起的,而是一种原来存在于InSb中的内在因素所起的作用,推测可能是与氧和氢有关。最后我们对解释这种热处理现象的可能的机理进行了探讨。     

Current progress on heat conduction in one-dimensional gas channels

We give a brief review of the past development of model studies on one-dimensional heat conduction. Particularly, we describe recent achievements on the study of heat conduction in one-dimensional gas models including the hard-point gas model and billiard gas channel. For a one-dimensional gas of elastically colliding particles of unequal masses, heat conduction is anomalous due to momentum conservation, and the divergence exponent of heat conductivity is estimated as α≈0.33 in k ∼ L ^α . Moreover, in billiard gas models, it is found that exponent instability is not necessary for normal heat conduction. The connection between heat conductivity and diffusion is investigated. Some new progress is reported. A recently proposed model with a quantized degree of freedom to study the heat transport in quasi-one dimensional systems is illustrated in which three distinct temperature regimes of heat conductivity are manifested. The establishment of local thermal equilibrium (LTE) in homogeneous and heterogeneous systems is also discussed. Finally, we give a summary with an outlook for further study about the problem of heat conduction.     

Estimation of the required collector area of a solar assisted heat pump

The solar assisted heat pump represents a method of increasing the heat pump COP by transferring solar radiation heat to the heat pump evaporator. In this paper a method of calculating the minimum design limit for the collector area based on the second law efficiency is introduced by using a set of experimental data on a certain design of a solar assisted heat pump system during winter time. A comparative study is made between the actual and ideal conditions, and a minimum required area of the collector is suggested.     

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.     

Speed-Dependent Weighting of the Maxwellian Distribution in Rarefied Gases: A Second-Law Paradox?

We show that the velocity distribution in rarefied (i.e., Knudsen) gases is spontaneously weighted in favor of small speeds away from the Maxwellian distribution corresponding to the temperature of the container walls—despite thermodynamic equilibrium with the walls. The consequent paradox concerning the second law of thermodynamics is discussed.