We revisit the optimization of performance of finite-time Carnot machines satisfying the low-dissipation assumption. The standard procedure seeks to optimize an objective function, such as power output of the engine, over the durations of contacts between the working medium and the heat reservoirs. This procedure may lead to unwieldy equations at the optimum of some objective functions. We propose an alternate scheme in which the output or input work is first optimized for a given cycle time, followed by an optimization of another objective function over the cycle time. The optimal behavior is thus obtained in a much simplified manner, with closed-form expressions for figures of merit. The approach is demonstrated for various objective functions, both for engines as well as refrigerators.
For the inverse square long-range ferromagnetic Ising chain in a transverse field, the thermal phase boundary of the floating Kosterlitz-Thouless phase is obtained for several values of the transverse field down to the quantum critical point. The sharp domain walls in the classical model are increasingly smeared out by the transverse field, which is evidenced by a pronounced broadening of the non-universal bump in the specific heat. The discernability of KT critical scaling in finite-size simulations is discussed.
In this paper, thermal transport in bond-disordered harmonic chains is revisited in detail using a nonequilibrium Green's function formalism. For strong bond disorder, thermal conductivity is independent of the system size. However, kinetic temperatures described by the local number of states coupling to external heat reservoirs are anomalous since they form a nonlinear profile in the interior of the system. Both results are accounted for in a unified manner in terms of the frequency-dependent localization length. From this argument, we derive a generic formula describing the asymptotic profil…
Einstein and Boltzmann: Determinism and Probability or The Virial Expansion Revisited
玻尔兹曼的原理S = k ln W多次受到爱因斯坦的批评，因为它缺乏适当的动力学基础，因为粒子的热运动是组成物理系统的基础。这特别表明，处于热平衡的系统的统计力学应该以动力学为基础。作为一个例子，动力学推导的密度展开的两个粒子的分布函数，以及一个中等密度的气体在热平衡的热力学性质，在这里概述。这是一个不同于通常的推导基于吉布斯的概率正则系综，其中动力学是消除在开始和平衡统计力学减少到静态。有人认为，本推导在本文中，在原则上，也可以适用于其他平衡性质，也许也适用于其他领域。
For systems in equilibrium at a temperature $T$, thermal noise and energy damping are related to $T$ through the fluctuation-dissipation theorem (FDT). We study here an extension of the FDT to an out of equilibrium steady state: a microcantilever subject to a constant heat flux. The resulting thermal profile in this spatially extended system interplays with the local energy dissipation field to prescribe the amplitude of mechanical fluctuations. Using three samples with different damping profiles (localized or distributed), we probe this approach and experimentally demonstrate the link between…
The thermal transport properties of a two dimensional Fermi gas are explored, for the full range of temperatures and densities. The heat flux is established by solving the Uehling-Uhlebeck equation using a relaxation approximation given by Marle's collisional kernel and considering the temperature and chemical potential gradients as independent thermodynamic forces. It is shown that the corresponding transport coefficients are proportional to each other, which leads to the possibility of defining a generalized thermal force and a single transport coefficient. The behavior of such conductivity …
For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of fields. Here we experimentally probe the relation between the number fluctuations and the response function for a Bose-Einstein condensate of photons coupled to a dye reservoir, demonstrating the fluctuation-dissipation relation for a quantum gas of light. The observed agreement of the scale factor with the environment temperature both directly confirms the therm…
