Free energy landscape from path-sampling: application to the structural transition in LJ38

We introduce a path-sampling scheme that allows equilibrium state-ensemble averages to be computed by means of a biased distribution of non-equilibrium paths. This non-equilibrium method is applied to the case of the 38-atom Lennard-Jones atomic cluster, which has a double-funnel energy landscape. We calculate the free energy profile along the Q₄ bond orientational order parameter. At high or moderate temperature the results obtained using the non-equilibrium approach are consistent with those obtained using conventional equilibrium methods, including parallel tempering and Wang-Landau Monte Carlo simulations. At lower temperatures, the non-equilibrium approach becomes more efficient in exploring the relevant inherent structures. In particular, the free energy agrees with the predictions of the harmonic superposition approximation.     

Thermodynamics of diffusive DM/DE systems

We discuss the energy density, temperature and entropy of dark matter (DM) and dark energy (DE) as functions of the scale factor a in an expanding universe. In a model of non-interacting dark components we repeat a derivation from thermodynamics of the well-known relations between the energy density, entropy and temperature. In particular, the entropy is constant as a consequence of the energy conservation. We consider a model of a DM/DE interaction where the DM energy density increase is proportional to the particle density. In such a model the dependence of the energy density and the temperature on the scale factor a is substantially modified. We discuss (as a realization of the model) DM which consists of relativistic particles diffusing in an environment of DE. The energy gained by the dark matter comes from a cosmological fluid with a negative pressure. We define the entropy and free energy of such a non-equilibrium system. We show that during the universe evolution the entropy of DM is increasing whereas the entropy of DE is decreasing. The total entropy can increase (in spite of the energy conservation) as the DM and DE temperatures are different. We discuss non-equilibrium thermodynamics on the basis of the notion of the relative entropy.     

Brownian system in energy space

The main goal of this article is to present a simple way to describe non-equilibrium systems in energy space and to obtain new spacial solution that complements recent results of B.I. Lev and A.D. Kiselev, Phys. Rev. E 82 , (2010) 031101. The novelty of this presentation is based on the kinetic equation which may be further used to describe the non-equilibrium systems, as Brownian system in the energy space. Starting with the basic kinetic equation and the Fokker-Plank equation for the distribution function of the macroscopic system in the energy space, we obtain steady states and fluctuation relations for the non-equilibrium systems. We further analyze properties of the stationary steady states and describe several nonlinear models of such systems.     

Rotational relaxation rates in CO-He mixtures

The rotational level populations of CO molecules were measured in CO(<10%) + He free jets by electron beam fluorescence (in a stationary jet) and resonantly enhanced multiphoton ionization (in a pulsed jet). The measured evolution of the non-equilibrium rotational energy was used to derive the rotational relaxation cross-sections in the temperature range from 6 K to 140 K. To compare and analyse on a common basis all available experimental data (ours and others) on rotational relaxation of CO in He, the infinite order sudden approximation was explored. The following quantities were investigated: integral rotationally inelastic cross-sections, state-to-state rate coefficients, rotational relaxation times, line broadening coefficients, and non-equilibrium rotational energy distributions in a free jet.     

Dynamically regulated energy barriers with violation of symmetry for reaction path

The motion of a particle on a flexible one-dimensional base is investigated numerically. It is regarded as a barrier-overcoming process in a multi-dimensional phase space. Driving the system far from equilibrium, a directional flow of the particle is observed. In order to understand the appearance of the directionality, two kinds of transition states for the barrier-overcoming process are considered particularly: one of which is for the overcoming process from left to right and the other from right to left. System's conformations for these two transitions are found to be identical at equilibrium, but become different at non-equilibrium, which means that the transition states become direction dependent. The energy barrier heights defined for the two transition states are found to account for biased reaction rates for the directional flow. Thus, the barrier heights work as activation energy extended to far from equilibrium. From the viewpoint of phase space, the directional dependence of the transition states is understood as the symmetry violation of the reaction paths, the route of the reaction being selected depending on the overcoming direction. It should be noted that such a selection is brought about by autonomous dynamics of the system itself. These results suggest the possibility to define an effective potential for a class of dynamical systems in non-equilibrium situations.     

Electron inelastic mean free paths and energy losses in solids II: Electron gas statistical model

A statistical model for the calculation of inelastic mean free paths and energy losses of electrons in solids is described. Results for the application of the model to the six solid media Al, Au, Ag, Cu, Ni, and Si are presented. Agreement between calculated mean free paths and experimental attenuation lengths indicates that the statistical model provides a useful method in the little-studied electron energy range from a few tens of electron volts to 10 keV.     

Cusp Singularities in Boundary-Driven Diffusive Systems

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be non-differentiable, a phenomenon that is unique to non-equilibrium systems, and discuss the types of models which display such singularities. The structure of these singularities is found to generically be a cusp, which can be described by a Landau free energy or, equivalently, by catastrophe theory. Connections with analogous results in systems with finite-dimensional phase spaces are drawn.     

Inequalities for Non-equilibrium Fluctuations of Work

Five previously unknown inequalities relating equilibrium free energy differences and non-equilibrium work fluctuations are derived, and lucid path to derivation of many similar inequalities is presented. These results are based upon combined exploitation of the Jarzynski equality and the generalization of the scheme for producing uncertainty-type inequalities due to H. Weyl. The inequalities may possibly lead to better understanding of behavior of the equilibrium free-energy estimators from non-equilibrium experimental data in many important applications concerning biological, chemical, and physical molecular processes.     

Fluctuations and large deviations in non-equilibrium systems

For systems in contact with two reservoirs at different densities or with two thermostats at different temperatures, the large deviation function of the density gives a possible way of extending the notion of free energy to non-equilibrium systems. This large deviation function of the density can be calculated explicitly for exclusion models in one dimension with open boundary conditions. For these models, one can also obtain the distribution of the current of particles flowing through the system and the results lead to a simple conjecture for the large deviation function of the current of more general diffusive systems.     

颗粒介质的结构及热力学

颗粒介质具有远程无序和近程有序的结构, 是产生动力学不均匀性(dynamical heterogeneity) 和复杂不可逆过程的根源. 本文分析了颗粒介质的结构特征、变形和能量耗散之间的内在关联, 讨论了颗粒介质的弹性, 提出了流变应变增量、耦合应变增量和弹性应变增量的应变增量分解方式. 沿用非平衡热力学框架, 引入表征运动无序的动理学颗粒温度T^k和表征弹性应力涨落的构型温度T^c, 作为非平衡态变量, 建立了双颗粒温度热力学(two-granular-temperature thermodynamics, TGT理论), 注重分析了不可逆过程中的热力学力和流, 并与著名的砂土内变量热力学进行了对比.     

Leptogenesis and CPT violation

We construct a model in which neutrinos and anti-neutrinos acquire the same mass but slightly different energy dispersion relations. Despite CPT violation, spin-statistics is preserved. We find that leptogenesis can be easily explained within this model, without upsetting the solar, atmospheric and reactor neutrino data. Leptogenesis occurs without lepton-number violation and the non-equilibrium condition. We consider only three active Dirac neutrinos, and no new particles or symmetries are introduced.     

Bulk Viscous Cosmological Model with Interacting Dark Fluids

We study a cosmological model for a spatially flat Universe whose constituents are a dark energy field and a matter field comprising baryons and dark matter. The constituents are assumed to interact with each other, and a non-equilibrium pressure is introduced to account for irreversible processes. We take the non-equilibrium pressure to be proportional to the Hubble parameter within the framework of a first-order thermodynamic theory. The dark energy and matter fields are coupled by their barotropic indexes, which depend on the ratio between their energy densities. We adjust the free parameters of the model to optimize the fits to the Hubble parameter data. We compare the viscous model with the non-viscous one, and show that the irreversible processes cause the dark-energy and matter-density parameters to become equal and the decelerated–accelerated transition to occur at earlier times. Furthermore, the density and deceleration parameters and the distance modulus have the correct behavior, consistent with a viable scenario of the present status of the Universe.     

Natural patterns of energy dispersal

Universal patterns such as power-law dependences, skewed distributions, tree-like structures, networks and spirals are associated with energy dispersal processes using the principle of least action. Also ubiquitous temporal courses such as sigmoid growth, bifurcations and chaos are ascribed to the decrease of free energy in the least time. Moreover, emergence of natural standards such as the common genetic code and chirality consensus of amino acids are understood to follow from the quest to maximize the dispersal of energy. Many mathematical functions that model natural patterns and processes are found as approximations of the evolutionary equation of motion that has been derived from statistical physics of open systems. The evolutionary processes can be described as flows of energy that run from high energy sources to low energy sinks in the least time. However, the equation of evolution cannot be solved in general because the flows of energy and their driving forces are inseparable. Since the energy of the system keeps changing, the paths of evolution cannot be integrated from a given initial state to a final state. Although evolutionary courses of these non-Hamiltonian systems with two or more alternative ways of dissipation cannot be predicted, the flows of energy will search and naturally select paths of least action, known as geodesics, to consume free energy in the least time. The scale-invariant natural patterns follow from this natural law that impinges on processes at all scales of space and time.     

Analytical and numerical approaches to calculating the escape function for the emission of medium-energy electrons from uniform specimens

A program for the simulation of electron transport by the Monte Carlo method has been developed. This program implies the model of single scattering and dielectric approach (to calculate the characteristics of an inelastic interaction). The escape functions for aluminum, germanium, and gold in the 0.012–20 keV energy range were calculated. The characteristic lengths determining the electron dynamics (the elastic and inelastic mean free paths, isotropization length, and integral path) were calculated using the differential cross sections for both elastic and inelastic interactions for these elements. The analysis of the relations between the characteristic lengths made it possible to determine the applicability range of the analytical expressions for the emission functions obtained in [1]. The comparison of the results obtained analytically and numerically confirmed the conclusion of [1] about the form of the analytical approximation of the emission function for electrons of various energies and showed the validity of the obtained analytical expressions for the escape lengths of electrons.     

关于热诱导一级相变过程的非平衡态理论

为了研究线性温度场条件下一级相变过程中的非平衡态特征，在相变系统的自由能中引入了一个附加项，该项与序参量对时间或温度的梯度有关．由此得到的数值解与实验观察到的一级相变过程中的非对称滞后行为相符合 关键词：     

Generalized Hellmann-Feynman Theorem for Coupled Anisotropic Two-Mode Boson System

We apply the Generalized Hellmann-Feynman theorem (GHFT) to calculate the thermodynamical relations of two-coupled anisotropic boson system by the method of characteristics. Its internal energy, Helmholtz free energy, and entropy in thermodynamics are obtained. It is found that GFHT is a new approach to directly calculate these thermodynamical functions.     

热漏、热阻及回热特性对磁Ericsson制冷循环最优性能的影响

建立了同时考虑热漏、热阻及回热等主要不可逆因素的顺磁质 Ericsson制冷循环的模型。针对回热平衡与回热不平衡的情况 ,应用有限时间热力学理论 ,导出了制冷率与制冷系数间的基本优化关系 ,给出了制冷率、制冷系数的优化值域 ,结果反映了回热式制冷机的主要观测特征。讨论了基本优化关系的应用 ,分析了热漏、热阻及回热损失对制冷循环性能影响的本质差异