Statistical thermodynamics of an anharmonic oscillator

In the present study we investigate the statistical thermodynamics of the anharmonic oscillator, whose energies are characterized by the potential 1/2x ²+x ⁴. Employing the energies recently obtained by Hioe and Montroll, we compute the partition function and the thermodynamic quantities for the anharmonic and quartic oscillators. Low- and high-temperature formulas are presented for the thermodynamic quantities of the oscillators.     

强关联费米气体的高温热力学性质

文章首先简要评述了目前强关联超冷费米原子体系的研究现状.由于缺少严格解和小相互作用参数,强关联的量子气体一直缺乏清晰的理解.在该项研究工作中,文章作者提出了一种系统的维里级数展开方法来研究强相互作用费米气体在高温下的热力学行为.方法中的控制小参量是易逸度,即exp(μ/kBT),其中μ是体系的化学势.文章提出了一种实用的方法去计算均匀或势阱束缚下的费米气体的维里展开系数,并首次精确得到了第三维里系数.文章将计算得到的热力学状态方程与最近的实验测量及量子蒙特卡罗模拟结果进行了比较.     

分析热力学的应用：平衡态热力学中温度的相对论变换

用分析热力学的观点和方法研究了温度的相对论变换公式，得到了与Planck，Einstein和de Broglie完全相同的结果：T=1-β²T₀；分析热力学的特色和 优点是，在推演过程 中根本不需要δQ=1-βδQ₀这一可能引起争议的和p=p₀这 一显而易见的相对论变换公式，它们是作为附带结果出现的. 关键词： 分析热力学 相对论热力学 平衡态热力学 热力学基本Poisson括号     

The discovery of thermodynamics

Abstract

Based on the idea that a scientific journal is also an “agora” (Greek: market place) for the exchange of ideas and scientific concepts, the history of thermodynamics between 1800 and 1910 as documented in the Philosophical Magazine Archives is uncovered. Famous scientists such as Joule, Thomson (Lord Kelvin), Clausius, Maxwell or Boltzmann shared this forum. Not always in the most friendly manner. It is interesting to find out, how difficult it was to describe in a scientific (mathematical) language a phenomenon like “heat”, to see, how long it took to arrive at one of the fundamental principles in physics: entropy. Scientific progress started from the simple rule of Boyle and Mariotte dating from the late eighteenth century and arrived in the twentieth century with the concept of probabilities. Thermodynamics was the driving intellectual force behind the industrial revolution, behind the enormous social changes caused by this revolution. The history of thermodynamics is a fascinating story, which also gives insights into the mechanism that seem to govern science.     

Black-hole thermodynamics: Entropy, information and beyond

We review some recent advances in black-hole thermodynamics including statistical mechanical origins of black-hole entropy and its leading order corrections from the view points of various quantum gravity theories. We then examine the problem of information loss and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.     

Mesoscopic transport equations and contemporary thermodynamics: an introduction

The local equilibrium hypothesis is a very successful basis for non-equilibrium thermodynamics over a wide range of phenomena and physical situations. However, the increasing interest in small systems in nanotechnology, in rarefied gases in high-altitude aeronautics, in high-frequency behaviour in information processing, or the search for new materials with sophisticated internal microstructures and tailored thermal properties have led one to ask about the limits of validity of this hypothesis, and to go beyond it. Here we do so in a constructive way, i.e. not only pointing out at these limits, but also embedding the local-equilibrium theory in a more general framework which explicitly exhibits these limits and suggests how to go beyond them, in search for a wider range of applications and a deeper understanding of the foundations.     

Quantum thermodynamics

Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations and with the full inclusion of quantum effects. Fuelled by experimental advances and the potential of future nanoscale applications, this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of ‘work’ to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.     

Universality in heat conduction theory: weakly nonlocal thermodynamics

A linear irreversible thermodynamic framework of heat conduction in rigid conductors is introduced. The deviation from local equilibrium is characterized by a single internal variable and a current multiplier. A general constitutive evolution equation of the current density of the internal energy is derived by introducing a linear relationship between the thermodynamic forces and fluxes. The well‐known Fourier, Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys‐type, and Green–Naghdi‐type equations of heat conduction are obtained as special cases. The universal character of the approach is demonstrated by two examples. Solutions illustrating the properties of the equation with jump boundary conditions are given.     

Pseudoelectrostatic effects in the thermodynamics of dye binding to DNA

Summary The interaction of DNA with the dye ethidium bromide (EB) has been investigated under the presence of methanol at varying temperatures. The Gibbs free energy associated with the DNA-EB binding is found to be well described by its linear dependence upon the dielectric constant of the solution, a property also found for other alcohols. When the enthalpy and entropy associated with the binding are considered, it is found that their role becomes rather simple if their evaluation is performed isodielectrically (ε=const). According to this procedure, the varying properties of the solvent can be separated from those of the interacting DNA and EB and the presence of hydrophobic interactions becomes then well established. Partially supported by Gruppo Nazionale Struttura della Materia, C.N.R.     

Universal thermodynamics in different gravity theories: Conditions for generalized second law of thermodynamics and thermodynamical equilibrium on the horizons

The present work deals with a detailed study of universal thermodynamics in different modified gravity theories. The validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) of the Universe bounded by a horizon (apparent/event) in f(R)$f\left(R\right)$-gravity, Einstein–Gauss–Bonnet gravity, RS-II brane scenario and DGP brane model has been investigated. In the perspective of recent observational evidences, the matter in the Universe is chosen as interacting holographic dark energy model. The entropy on the horizons is evaluated from the validity of the unified first law and as a result there is a correction (in integral form) to the usual Bekenstein entropy. The other thermodynamical parameter namely temperature on the horizon is chosen as the recently introduced corrected Hawking temperature. The above thermodynamical analysis is done for homogeneous and isotropic flat FLRW model of the Universe. The restrictions for the validity of GSLT and the TE are presented in tabular form for each gravity theory. Finally, due to complicated expressions, the validity of GSLT and TE are also examined from graphical representation, using three Planck data sets.     

The Young-Hoshino pseudopotential for lithium: calculations of structure and thermodynamics

The recently proposed Young-Hoshino model pseudopotential for lithium has been applied to the calculation of structure and thermodynamics. A slight modification of the model potential is necessary and this produces better core size and long range tail of the interionic effective pair potential than the original model.     

Generalized surface thermodynamics with application to nucleation

Gibbs formulated a complete and general thermodynamics for surfaces in multicomponent fluid systems. When considering solid–fluid surfaces, he restricted attention to single-component solids in contact with fluids that could contain multiple components. Attempts that have been offered to generalize Gibbs’ results for surfaces between multicomponent solids and fluid are problematic owing to the difficulty that the surface chemical potentials for components that also reside on substitutional lattice sites in the solids are not well defined. Therefore any expressions involving these surface chemical potentials, such as the conventional definition of the surface energy, will also not be well defined. In order to formulate a general thermodynamics of equilibrium that takes into account capillary effects in systems containing surfaces between a multicomponent solids and fluids, it is shown that the concept of thermodynamic availability (exergy) can be employed that, when applied to surfaces, depends on the extensive but not the intensive variables (such as the chemical potentials) of the surfaces. Using this approach, Gibbs–Thomson–Freundlich effects for finite-size solids, an adsorption equation for solid–fluid surfaces and the thermodynamics of nucleation during solidification can be treated in a straightforward manner without referring to the ill-defined surface chemical potentials. A derivation is given that appears to be the first one that properly generalizes Gibbs’ analysis for the reversible work to form a critical nucleus to the case of solidification.     

Problems of nonextensivity in hadron thermodynamics

Hadron thermodynamics deals with a gas of indistinguishable particles whose mass spectrum is taken to have the formKm ^a e ^bm . A long-standing inconsistency is pointed out, namely the nonextensive nature of the entropy found in some treatments by way of the microcanonical ensemble, which contrasts with the extensive nature found by way of the canonical ensemble. The former result is due to an error. After correction, the two ensembles are found to lead to the same expressions for the thermodynamic quantities ifa –7/2. Some of these expressions are new. Fora<–5/2, the microcanonical approach is used to examine a model in which one particle is appreciably heavier than the rest. However, the resulting entropy is found to be unphysical.     

Grad theory and extended thermodynamics

Grad-type approaches introduce an ansatz involving tensor Hermite functions with coefficients expresed in terms of moments of the ansatz. This formalism in usual form yields terms linear in first-order spatial derivatives in kinetic equations for the moments. Such terms disagree with alternative statistical derivations and phenomenological arguments. This disagreement is removed if different ansatzes are used to calculate entropy and moment equations. These are non-unique, and so Grad theory, while providing theoretical expressions for transport coefficients, does not serve uniquely to determine the structure of phenomenological equations.     

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.     

Entropy identity and equilibrium conditions in relativistic thermodynamics

Starting out with the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a framework for special- and general-relativistic continuum thermodynamics. A general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced. This makes possible, firstly, to test special entropy density 4-vectors used by other authors with respect to their generality and validity and, secondly, to determine entropy supply and entropy production. Using this entropy density 4-vector, material-independent equilibrium conditions are discussed. While in literature, generally thermodynamic equilibrium is determined by introducing a variety of conditions by hand, the present approach proceeds as follows: For a comparatively wide class of space–time geometries, the necessary equilibrium conditions of vanishing entropy supply and vanishing entropy production are exploited. Because these necessary equilibrium conditions do not determine the equilibrium, supplementary conditions are added systematically motivated by the requirement that also all parts of the necessary conditions have to be fixed in equilibrium.     

Self‐assembled silver nanoparticle monolayer on glassy carbon: an approach to SERS substrate

In this paper, the fabrication of an active surface‐enhanced Raman scattering (SERS) substrate by self‐assembled silver nanoparticles on a monolayer of 4‐aminophenyl‐group‐modified glassy carbon (GC) is reported. Silver nanoparticles are attached to the substrate through the electrostatic force between the negatively charged silver nanoparticles and the positively charged 4‐aminophenyl groups on GC. The active SERS substrate has been characterized by means of tapping‐mode atomic force microscopy (AFM), indicating that large quantities of silver nanoparticles are uniformly coated on the substrate. Rhodamine 6G (R6G) and p‐aminothiophenol (p‐ATP) are used as the probe molecules for SERS, resulting in high sensitivity to the SERS response, with the detection limit reaching as low as 10⁻⁹ M . This approach is easily controlled and reproducible, and more importantly, can extend the range of usable substrates to carbon‐based materials for SERS with high sensitivity. Copyright © 2007 John Wiley & Sons, Ltd.