Nonequilibrium Statistical Thermodynamics Research Articles

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 3—Taylor–Quinney coefficient, size effects and generalized normality

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 3—Taylor–Quinney coefficient, size effects and generalized normality

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 1: subsystem reactions under constrained local equilibrium

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 1: subsystem reactions under constrained local equilibrium

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 2—ensemble evolution toward correlation of enthalpy barriers

Nonequilibrium statistical thermodynamics of thermally activated dislocation ensembles: part 2—ensemble evolution toward correlation of enthalpy barriers

FECOCRNIMOTIW HIGH-ENTROPIC COATINGS AND THEIR PROPERTIES

The objects of study were high-entropy coatings of the composition FeCoCrNiMoTiW made by mechanical alloying. It is shown that the hardness of most stainless steels is 1.5-2 times less than high-entropy coatings, and the dry friction coefficients are in the range of 0.08-0.16. Such a difference in the coefficients of friction for high-entropy coatings is due to their nanostructural feature and the manifestation of the dimensional dependence of their properties. Theoretically, we consider the question of the response of the electron subsystem in high-entropy alloys to an external action during friction from the standpoint of nonequilibrium statistical thermodynamics. As a result, it was shown that the coefficient of friction of the coating decreases with the use of a high-entropy alloy and with a decrease in the surface energy of the coating.

Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

In the context of a nonequilibrium statistical thermodynamics, based on a nonequilibrium statistical ensemble formalism, a generalized hydrodynamics of fluids under driven flow and shear stress is derived. At the thermodynamic level, the nonequilibrium equations of state are derived, which are coupled to the evolution of the basic variables that describe the hydrodynamic motion in such a system. Generalized diffusion-advection and Maxwell-Cattaneo advection equations are obtained in appropriate limiting situations. This nonlinear higher-order hydrodynamics is applied, in an illustration, to the case of a dilute solution of Brownian particles in nonequilibrium conditions and flowing in a solvent acting as a thermal bath. This is done in the framework of such generalized hydrodynamics but truncated up to a second order.

Rational analysis of processes of (first-order) ferroelectric phase transition and those of ferroic hysteresis

From the view-point of non-equilibrium (or irreversible) statistical thermodynamics, the similarities and differences between the processes of (first-order) ferroelectric phase transition and those of ferroic hysteresis were compared. They are all irreversible. The former are local and rate-dependent, at the meanwhile, the latter are non-local and rate-independent.

Деканалирование высокоэнергетических частиц из плоскостных каналов кристалла. Упругие и неупругие процессы рассеяния

Based on the principles of nonequilibrium statistical thermodynamics, the kinetic theory of de-channeling of high-energy particles from planar channels of a crystal have been deduced. The de-channeling rate coefficient is considered from the point of view of the transition of a fast particle from the directional motion mode to the state of chaotic motion. The corresponding equation have been obtained that takes into account both the coherent nature of the diffraction of a particle beam in a regular single crystal and the inelastic scattering of channeled particles by electrons and phonons. An analytical solution of this equation have been obtained on the class of confluent hypergeometric function using which the de-channeling rate constant Re have been calculated. It have been shown that up to second-order terms in terms of the interaction potential the constant Re is inversely proportional to the relaxation time of the system tph. In calculating tph the polarization of space by a fast charged particle is not taken into account. The temperature and isotopic dependences of the de-channeling rate have been obtained.

Entropy Production, Entropy Generation, and Fokker-Planck Equations for Cancer Cell Growth

It is rather difficult to understand biological systems from a physics point of view, and understanding systems such as cancer is even more challenging. There are many factors affecting the dynamics of a cancer cell, and they can be understood approximately. We can apply the principles of non-equilibrium statistical mechanics and thermodynamics to have a greater understanding of such systems. Very much like other systems, living systems also transform energy and matter during metabolism, and according to the First Law of Thermodynamics, this could be described as a capacity to transform energy in a controlled way. The properties of cancer cells are different from regular cells. Cancer is a name used for a set of malignant cells that lost control over normal growth. Cancer can be described as an open, complex, dynamic, and self-organizing system. Cancer is considered as a non-linear dynamic system, which can be explained to a good degree using techniques from non-equilibrium statistical mechanics and thermodynamics. We will also look at such a system through its entropy due to to the interaction with the environment and within the system itself. Here, we have studied the entropy generation versus the entropy production approach, and have calculated the entropy of growth of cancer cells using Fokker-Planck equations.

Optically controlled stochastic jumps of individual gold nanorod rotary motors

Brownian microparticles diffusing in optical potential energy landscapes constitute a generic testbed for nonequilibrium statistical thermodynamics and has been used to emulate a wide variety of physical systems, ranging from Josephson junctions to Stirling engines. Here we demonstrate that it is possible to scale down this approach to nanometric length-scales by constructing a tilted washboard potential for the rotation of plasmonic gold nanorods. The potential depth and tilt can be precisely adjusted by modulating the light polarization. This allows for a gradual transition from continuous rotation to discrete stochastic jumps, which are found to follow Kramers dynamics in excellent agreement with stochastic simulations. The results widen the possibilities for fundamental experiments in statistical physics and provide new insights in how to construct light-driven nanomachines and multifunctional sensing elements.

Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations

We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrodinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.

Structural transition of solvated H-Ras/GTP revealed by molecular dynamics simulation and local network entropy

The state transitions of solvated H-Ras protein with GTP were theoretically analyzed through molecular dynamics (MD) simulations. To accelerate the structural changes associated with the locations of two switch regions (I and II), the Parallel Cascade Selection MD (PaCS-MD) method was employed in this study. The interconversions between the State 1 and State 2 were thus studied in atomic details, leading to a reasonable agreement with experimental observations and consequent scenarios concerning the transition mechanism that would be essential for the development of Ras inhibitors as anti-cancer agents. Furthermore, the state-transition-based local network entropy (SNE) was calculated for the transition process from State 1 to State 2, by which the temporal evolution of information entropy associated with the dynamical behavior of hydrogen bond network composed of hydration water molecules was described. The calculated results of SNE thus proved to provide a good indicator to detect the dynamical state transition of solvated Ras protein system (and probably more general systems) from a viewpoint of nonequilibrium statistical thermodynamics.

Impact of external influences on characteristics of domains in biological membranes

Living systems continually interact with the environment. External influences evoke complex processes in the entire system. In this work, the impact of external influences on the behavior of the domains in biological membranes is considered both in general and on special examples. A general approach of nonequilibrium statistical thermodynamics proposed by L.A. Stratonovich along with the same approach adapted to stochastic storage processes are applied. Both the Stratonovich theory and the storage models allow characterizing specific features of the stationary non-equilibrium states as well as the behavior of the highly non-equilibrium processes in open systems, such as live organisms.

Diffusion mobility of the hydrogen atom with allowance for the anharmonic attenuation of migrating atom state

Evolution of vibration relaxation of hydrogen atoms in metals with the close-packed lattice at high and medium temperatures is investigated based on non-equilibrium statistical thermodynamics, in that number on using the retarded two-time Green function method. In accordance with main kinetic equation – the generalized Fokker- Plank- Kolmogorov equation, anharmonism of hydrogen atoms vibration in potential wells does not make any contribution to collision effects. It influences the relaxation processes at the expense of interference of fourth order anharmonism with single-phonon scattering on impurity hydrogen atoms. Therefore, the total relaxation time of vibration energy of system metal-hydrogen is written as a product of two factors: relaxation time of system in harmonic approximation and dimensionless anharmonic attenuation of quantum hydrogen state.

Predictive Statistical Mechanics and Macroscopic Time Evolution: Hydrodynamics and Entropy Production

In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy, subject to the constraint given by the Liouville equation averaged over the phase space, leads to a definition of the rate of entropy change for closed Hamiltonian systems without any additional assumptions. Here, we generalize this basic model and, with the introduction of the additional constraints which are equivalent to the hydrodynamic continuity equations, show that the results obtained are consistent with the known results from the nonequilibrium statistical mechanics and thermodynamics of irreversible processes. In this way, as a part of the approach developed in this paper, the rate of entropy change and entropy production density for the classical Hamiltonian fluid are obtained. The results obtained suggest the general applicability of the foundational principles of predictive statistical mechanics and their importance for the theory of irreversibility.

A numerical method for the time coarsening of transport processes at the atomistic scale

We propose a novel numerical scheme for the simulation of slow transport processes at the atomistic scale. The scheme is based on a model for non-equilibrium statistical thermodynamics recently proposed by the authors, and extends it by formulating a variational integrator, i.e. a discrete functional whose optimality conditions provide all the governing equations of the problem. The method is employed to study surface segregation of AuAg alloys and its convergence is confirmed numerically.

Atomistic long-term simulation of heat and mass transport

We formulate a theory of non-equilibrium statistical thermodynamics for ensembles of atoms or molecules. The theory is an application of Jaynes׳ maximum entropy principle, which allows the statistical treatment of systems away from equilibrium. In particular, neither temperature nor atomic fractions are required to be uniform but instead are allowed to take different values from particle to particle. In addition, following the Coleman–Noll method of continuum thermodynamics we derive a dissipation inequality expressed in terms of discrete thermodynamic fluxes and forces. This discrete dissipation inequality effectively sets the structure for discrete kinetic potentials that couple the microscopic field rates to the corresponding driving forces, thus resulting in a closed set of equations governing the evolution of the system. We complement the general theory with a variational meanfield theory that provides a basis for the formulation of computationally tractable approximations. We present several validation cases, concerned with equilibrium properties of alloys, heat conduction in silicon nanowires and hydrogen desorption from palladium thin films, that demonstrate the range and scope of the method and assess its fidelity and predictiveness. These validation cases are characterized by the need or desirability to account for atomic-level properties while simultaneously entailing time scales much longer than those accessible to direct molecular dynamics. The ability of simple meanfield models and discrete kinetic laws to reproduce equilibrium properties and long-term behavior of complex systems is remarkable.

Macroscopic approach to the Casimir friction force

The general formula is derived for the vacuum friction force between two parallel perfectly flat planes bounding two material media separated by a vacuum gap and moving relative to each other with a constant velocity $\mathbf{v}$. The material media are described in the framework of macroscopic electrodynamics whereas the nonzero temperature and dissipation are taken into account by making use of the Kubo formulae from non-equilibrium statistical thermodynamics. The formula obtained provides a rigorous basis for calculation of the vacuum friction force within the quantum field theory methods in the condensed matter physics. The revealed $v$-dependence of the vacuum friction force proves to be the following: for zero temperature ($T=0$) it is proportional to $(v/c)^3$ and for $T>0$ this force is linear in $(v/c)$.

NONEQUILIBRIUM THERMODYNAMICS: A POWER FUL TOOL FOR SCIENTISTS AND ENGINEERS

We present the two-generator framework of nonequilibrium thermodynamics with a strong emphasis on fundamental notions rather than mathematical details. The underlying sta- tistical mechanics and the implications for thermodynamically guided simulation techniques are sketched briefly. The usefulness and maturity of the framework are illustrated by reviewing a large number of recent far- from-equilibrium applications, where nonlinearity rules. Finally, we oter some promising perspectives for the future of nonequilibrium thermodynamics. I. INTRODUCTION Thermodynamics occurs in the curriculum of every sci- entist or engineer. A typical course on thermodynamics restricted to equilibrium phenomena. In most mod- ern courses, thermodynamics presented together with statistical mechanics; in many cases, statistical mechan- ics even presented in the beginning of the course, as if thermodynamics could be derived from statistical me- chanics. Historically, thermodynamics has of course been developed well before statistical mechanics, based on a multitude of experimental observations condensed into the fundamental laws of equilibrium thermodynamics. Moreover, thermodynamics has the beautiful geometric structure associated with Legendre transformations be- tween pairs of conjugate extensive and intensive variables (contact structure) and a full-fledged theory in its own right. Whereas thermodynamics usually not among the most popular courses, its laws and tools eventually prove useful to most scientists and engineers. In many applica- tions, however, one would like to go beyond equilibrium thermodynamics. A typical example provided by trans- port phenomena (1) which play a most important role in biology, chemical engineering, materials processing, me- chanical engineering, and many other fields. Relaxation phenomena occurring in many areas of application also belong to the world of nonequilibrium thermodynamics. Simplification by coarse-graining the description and fo- cusing on the essence of a problem an important key to successful engineering. A general course on statistical nonequilibrium thermodynamics would hence be at least as useful as a course on equilibrium thermodynamics. The purpose of this article to address the ques- tion is nonequilibrium thermodynamics ready for sci- entists and engineers? Should a corresponding course occur in a state-of-the-art curriculum in science and en- gineering? To answer this question we describe a lu- cent framework of nonequilibrium thermodynamic and its statistical-mechanical foundations. We then provide a number of recent applications of this framework. We finally offer some conclusions and an outlook. This article may be considered as a continuation of the compact review (2) presenting modern nonequilibrium thermodynamics to applied scientists and engineers. We hence focus on collecting the literature on the new developments mainly of the last 10 years.

Supercritical fluid thermodynamics from equations of state

Supercritical multicomponent fluid thermodynamics are often built from equations of state. We investigate mathematically such a construction of a Gibbsian thermodynamics compatible at low density with that of ideal gas mixtures starting from a pressure law. We further study the structure of chemical production rates obtained from nonequilibrium statistical thermodynamics. As a typical application, we consider the Soave–Redlich–Kwong cubic equation of state and investigate mathematically the corresponding thermodynamics. This thermodynamics is then used to study the stability of H2–O2–N2 mixtures at high pressure and low temperature as well as to illustrate the role of nonidealities in a transcritical H2–O2–N2 flame.

Balance equation and the quasitemperature of channeled particles in equilibrium

Using the methods of nonequilibrium statistical thermodynamics, we obtain the equation for the transverse energy and momentum balance for fast atomic particles moving in the planar channeling regime. Based on the solution of this equation, we obtain an expression for the transverse quasitemperature in the quasiequilibrium in terms of the basic parameters of the theory. We show that the equilibrium quasitemperature of channeled particles is established because of particle diffusion in the space of transverse energies (subsystem “heating”), the dissipative process (“cooling”), and the anharmonic effects of particle oscillations between the channel walls (the redistribution of energies over the oscillatory degrees of freedom is the internal thermalization of the subsystem). According to the estimates for particles with an energy of the order of 1 MeV, the quasitemperature values are in the characteristic temperature range for a low-temperature plasma.