Thermodynamics Of Nonequilibrium Processes Research Articles

Transitions between equilibrium and nonequilibrium phenomena in the description of crystal growth

The close intertwining of equilibrium and nonequilibrium thermodynamic representations and transitions between the two limiting principles of thermodynamics: the second beginning and the principle of least coercion (minimum entropy production in the stationary regime) constitute the main content of phenomenological theories of crystal growth. The difference of basic postulates of two sections of thermodynamics forces to discuss problems of reversibility and irreversibility of time, scales of observed phenomena and rules of conjugation of thermodynamic forces and flows in theories of crystal growth. A variant of the solution of some conjugation problems is shown on the example of the fluctuation model of dislocation crystal growth, which is based on the stationary isothermal process of thermodynamic free energy fluctuations. In the case of the limiting mode of adsorption of impurities on the crystal face according to the Langmuir model, the free energy fluctuations possessing the absence of the memory effect allow us to identify three chemical potentials of building particles that determine the corresponding values of solution supersaturations realized at different scale levels at the growing crystal face containing a helical dislocation. The supersaturations control quasi-equilibrium and nonequilibrium thermodynamic processes that constitute a single dislocation mechanism of crystal growth.

Free Energy Differences in Nonequilibrium Thermodynamic Processes.

Systems which may be allowed to go out of equilibrium have been of interest recently. A quantity is formulated whose average over an ensemble of microscopic realizations of the process depends only on the initial and final states. This is so even though the system may not be in equilibrium during the process. A generalization to the case where the initial and final states are not equilibrium states is developed here. Quantum analogues of these relations are derived, and an indication of how this might be applied to study entropy increase in thermodynamics is presented.

The variational approach to study the mixed convection boundary layer flow over a permeable Riga plate

AbstractThe physical problem of steady state, laminar, mixed convection (Ri) with double‐diffusive (N) in an electrically low conducting fluid past a semi‐infinite electromagnetic () influenced flat plate with internal uniform heat generation (Q) in the presence of suction/injection (H) by considering viscous dissipation (Ec), thermophoresis (Nt) and thermal diffusion effects (Sr) is mathematically modeled as a simultaneous system of nonlinear partial differential equations. To achieve the solution of the problem numerically, Gyarmati's variational principle known as the “Governing Principle of Dissipative Processes” on the basis of nonequilibrium thermodynamic processes in the theory of continua, is adopted. This research work correlates the phenomenon of fluid around submersibles/space vehicles and provides related insights. To estimate the transportation fluid fields within the boundary layer, the appropriate trial polynomials have been employed, and functionals for the integral variational principle are determined. Next, the Euler–Lagrange equations of the functionals are obtained as a system of polynomial equations involving boundary layer thicknesses of momentum, temperature, and concentration. The expressions of local shear stress, local Nusselt, and local Sherwood numbers have been derived and the effects of various physical factors involved in the problem are explored. A comparison with the previously published results in the literature is provided to confirm the validity of the solution procedure. The results depict that injection () and opposing buoyancy () decrease the skin friction about 38% in sea water and 11% in ionized air when compared to impermeable plate for . The aiding buoyancy () plays a dominant role in heat and mass transfers, respectively, with the massive gradients of 340% and 763% in magnitude for the heavier fluid sea water flow while 47% and 3% for the lighter fluid ionized air flow when . The buoyancy parameters (Ri, N) decrease the heat transfer, but increase the mass transfer.

Dynamics of Cu–Zr metallic glass devitrification under ultrafast laser excitation revealed by atomistic modeling

The physics of metallic glass local devitrification employing ultrafast laser irradiation is the cradle of complex phenomena that are still not understood despite its applicative potential in material processing for nanotechnology. This paper reports a theoretical simulation combining the two temperature model and classical molecular dynamics simulations to unravel the mechanisms that lead to the localized phase transition in Cu–Zr metallic glass. According to observations, the initial composition of amorphous samples plays an essential role, in addition to nonequilibrium thermodynamic processes caused by the laser energy deposition that alters the atomic environment. We further demonstrate that specific compositions devitrify despite its high glass-forming ability. The thermodynamic conditions fostering the emergence of a stable nanocrystalline phase are clearly established. The compressive pressure wave and the rapid heating process caused by ultrafast laser energy deposition synergistically contribute to disrupt the microstructure of the glass significantly, thereby initiating the devitrification process. Results are discussed using additional classical MD simulations that provide valuable insights for interpreting the distinct contributions of temperature and pressure to the phase transformation. Finally, the impact of the formed nanocrystals on the phononic thermal conductivity of the alloy is presented confirming the potential application of the laser-induced devitrification process for the development of a new generation of nanoarchitectured materials.

Single-atom exploration of optimized nonequilibrium quantum thermodynamics by reinforcement learning

Exploring optimized processes of thermodynamics at microscale is vital to exploitation of quantum advantages relevant to microscopic machines and quantum information processing. Here, we experimentally execute a reinforcement learning strategy, using a single trapped 40Ca+ ion, for engineering quantum state evolution out of thermal equilibrium. We consider a qubit system coupled to classical and quantum baths, respectively, the former of which is achieved by switching on the spontaneous emission relevant to the qubit and the latter of which is made based on a Jaynes-Cummings model involving the qubit and the vibrational degree of freedom of the ion. Our optimized operations make use of the external control on the qubit, designed by the reinforcement learning approach. In comparison to the conventional situation of free evolution subject to the same Hamiltonian of interest, our experimental implementation presents the evolution of the states with higher fidelity while with less consumption of entropy production and work, highlighting the potential of reinforcement learning in accomplishment of optimized nonequilibrium thermodynamic processes at atomic level.

Investigation of non-uniform oxidation based on a mechanochemical phase field model with nonlinear reaction kinetics and large inelastic deformation

A mechanochemical model is proposed to investigate the non-uniform oxidation of thermal barrier coatings (TBCs) that involves large inelastic deformation and nonlinear reaction kinetics. The large-deformation theory incorporates the higher-order term of geometric nonlinearity for a more precise description of the deformation and stress evolution in an oxide layer. The effect of stresses on the reaction kinetics is considered, which is expressed as the Eshelby stress tensor to account for the conformational volume change and deformation energy. A nonlinear reaction kinetics is adopted for a more accurate description of the nonequilibrium thermodynamic processes. The 2D simulations reveal a non-uniform oxide growth, three modes of oxide-metal interfacial morphology evolution, and tensile stress concentrations in the oxide scale. These simulation results agree with the experimental observations that cannot be described by the previous models. With the model, it is further demonstrated that a stable interfacial morphology and a significantly reduced tensile stress can be achieved by increasing the creep rate of the oxide and the flatness of the oxide-metal interface. This model thus provides an approach to extend the service time of TBCs.

Quantum mechanics of open systems: Dissipaton theories.

This Perspective presents a comprehensive account of the dissipaton theories developed in our group since 2014, including the physical picture of dissipatons and the phase-space dissipaton algebra. The dissipaton-equation-of-motion-space (DEOM-space) formulations cover the Schrödinger picture, the Heisenberg picture, and further the imaginary-time DEOM. Recently developed are the dissipaton theories for studying equilibrium and nonequilibrium thermodynamic mixing processes. The Jarzynski equality and Crooks relation are accurately reproduced numerically. It is anticipated that dissipaton theories would remain essential toward a maturation of quantum mechanics of open systems.

Electrical Discharge Induced Bulk‐to‐Nanoparticle Transformation: Nano High‐Entropy Carbide as Catalysts for Hydrogen Evolution Reaction

AbstractHigh‐entropy carbide (HEC) is a promising alternative to precious metal catalysts for the hydrogen evolution reaction (HER). However, the preparation of nanoscale HECs is a great challenge although many methods have been developed to prepare bulk HEC materials. Herein, an electrical discharge induced bulk‐to‐nanoparticle transformation method is reported, by which well dispersed sub‐10 nm high entropy (MoWVNbTa)C nanoparticles with high‐density surface defects can be directly obtained by centrifugation of the waste liquid produced during wire‐cut electrical discharge machining of bulk HEC. The resultant HEC nanoparticles exhibit excellent catalytic activity and durability for HER, which is attributed to the combination of unique microstructure generated during the extremely nonequilibrium thermodynamic process and enhanced electronic effects induced by high configurational entropy. This facile and cost‐effective bulk‐to‐nanoparticle transformation method can be extended to other conductive materials and shed light on the development of high‐performance catalysts.

A Cell Model of an Ion-Exchange Membrane. Capillary-Osmosis and Reverse-Osmosis Coefficients

The capillary-osmosis and reverse-osmosis coefficients of an ion-exchange membrane have been calculated as the kinetic coefficients of the Onsager matrix within the thermodynamics of nonequilibrium processes and on the basis of the cell model proposed previously by the author for charged porous layers. The membrane is assumed to consist of an ordered set of spherical completely porous charged particles placed into spherical shells filled with a binary electrolyte solution. Boundary value problems have been analytically solved to determine the capillary-osmosis and reverse-osmosis coefficients of such a membrane under the Kuwabara boundary condition imposed on the cell surface. The consideration has been implemented within the framework of small deviations of system parameters from their equilibrium values under the action of external fields. Different particular cases of the obtained exact analytical equations have been studied including the case of a binary symmetric electrolyte and an ideally selective membrane. It has been shown that, for the considered cell model of an ion-exchange membrane, the Onsager reciprocity theorem is violated; i.e., the found kinetic cross coefficients are unequal to each other. The violation is explained by the fact that the reciprocity theorem is valid only for systems implying the linear thermodynamics of irreversible processes, for which generalized flows are equal to zero at nonzero thermodynamic forces.

Nonequilibrium thermodynamic process with hysteresis and metastable states—A contact Hamiltonian with unstable and stable segments of a Legendre submanifold

In this paper, a dynamical process in a statistical thermodynamic system of spins exhibiting a phase transition is described on a contact manifold, where such a dynamical process is a process that a metastable equilibrium state evolves into the most stable symmetry broken equilibrium state. Metastable and the most stable equilibrium states in the symmetry broken phase or ordered phase are assumed to be described as pruned projections of Legendre submanifolds of contact manifolds, where these pruned projections of the submanifolds express hysteresis and pseudo-free energy curves. Singularities associated with phase transitions are naturally arose in this framework as has been suggested by Legendre singularity theory. Then, a particular contact Hamiltonian vector field is proposed so that a pruned segment of the projected Legendre submanifold is a stable fixed point set in a region of a contact manifold and that another pruned segment is a unstable fixed point set. This contact Hamiltonian vector field is identified with a dynamical process departing from a metastable equilibrium state to the most stable equilibrium one. To show the statements above explicitly, an Ising type spin model with long-range interactions, called the Husimi–Temperley model, is focused, where this model exhibits a phase transition.

The study of the instability during the turning of heat resistant steels and alloys

The results of theoretical and experimental studies of contact phenomena in blade cutting based on the thermodynamics of non-equilibrium processes and from the standpoint of self-organization of the tribosystem are presented. the developed thermodynamic model of blade processing with variable cutting modes (non-stationary) allows to minimize the wear of the cutting tool and generally increase production effi ciency by accelerating the drive of the main movement of the metal-cutting machine.

Dynamics of the catalyst deactivation: tutorial experience with formalism of thermodynamics of non-equilibrium processes

The catalytic process, during which the catalyst loses activity, is usually difficult for investigation and industrial application, especially when the life time of the catalyst is relatively long (10 to 104 h). Therefore, experimental studies of the deactivation kinetics are very expensive, and mathematical modeling and simulation of the deactivation mechanisms becomes more significant, even more than models of reaction mechanisms. In this paper we present an approach to developing and analysis of deactivation dynamics models based on formalism of thermodynamics of non-equilibrium processes. The simplest two step sequence mechanism of the target reaction is used for deriving and analyzing models of reversible and irreversible deactivation mechanisms corresponding to poisoning and coking phenomena. Differential equations for dynamics of the key deactivation intermediate and of the target reaction rate, as well as of the catalyst relative activity are derived and solved. It is shown that thermodynamic formalism coupled with classic kinetic consideration is useful for the analysis of optimal bond energy of key intermediate with the catalyst, which can provide low deactivation.

Verification of finite bath fluctuation theorem for a non-ergodic system

The analysis of fluctuations generated by a thermal reservoir has produced many results throughout the history of science, ranging from the verification of the atomic hypothesis, running through critical phenomena to the most recent advances in the description of non-equilibrium thermodynamic processes. Motivated by recent theoretical and experimental works, we analyze the non-equilibrium and equilibrium fluctuations caused by a finite and chaotic heat bath in a simple system of interest. The finite bath and system of interest give rise to a non-ergodic composite system when interacting with each other. We have characterized the equilibrium distribution induced by the finite bath and numerically verified the finite-bath fluctuation theorem. We have also verified the convergence of our results to Crooks’ fluctuation theorem as the number of degrees of freedom of the finite bath increases while the non-ergodic character remains.

Path-integral approach to the calculation of the characteristic function of work.

Work statistics characterizes important features of a nonequilibrium thermodynamic process, but the calculation of the work statistics in an arbitrary nonequilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynman's path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schrödinger's formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach for the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.

Modeling of the Stressed and Phase States of Titanium-Nickelide Plates Under Thermomechanical Loading

On the basis of the proposed model, we study the phase and stressed states of titanium-nickelide plates under the conditions of bending and heating-and-cooling by using the methods of continuum mechanics and thermodynamics of nonequilibrium processes with an aim to get a quantitative description of the behavior of bodies made of shape memory materials. We perform calculations for various combinations of mechanical loads and temperatures. It is shown that, under the conditions of phase transformations in the plate, we observe the appearance of a distribution of martensite with variable thickness, which leads to the formation of an inhomogeneous residual stress-strain state.

A general thermodynamic law for multi-phase systems without turbulences in the non-linear regime and its application to separation processes

Prigogine's principle of minimum entropy production is valid only for single-phase thermodynamic systems with non-equilibrium stationary states in the linear regime. We will show that it can be generalized to a more general law in the non-linear regime for multi-phase thermodynamic systems without turbulences in the flow quantities. We take the example of fluid-mixture separation of the binary fluid mixture benzene-trichloroethylene in a distillation column, which is driven always with constant power in the various rectification processes. We will demonstrate that there are lots of stationary states depending on the additional free parameter of the return ratio of the liquid and vapor flow. We will show further that there is always one stationary state with minimum entropy production. This state corresponds to the optimum separation condition of the column and it is the one, which has the longest setting time. Although engineers use well-known, empirically found relations and equations for their calculations to optimize rectification processes, this new fundamental law of non-equilibrium thermodynamics for non-linear multi-phase systems with laminar flow quantities rationalizes the engineers' empirical knowledge. We will demonstrate that optimizing non-linear non-equilibrium multi-phase thermodynamic processes is based on maximization of entropy flow and minimization of entropy production, which corresponds to maximum reversible separation work for all kinds of separation processes. All performed calculations are based on rigorous thermodynamics. In following papers, we will show that this new discovery is valid for a broad range of non-linear open thermodynamic multi-phase processes and can be beneficially used, e.g. for optimizing chemical and biochemical processes.

POSSIBILITIES OF INTEGRATED CONTROL OF ENERGY AND ENVIRONMENTAL CHARACTERISTICS OF BUILDING STRUCTURES AT THE RESEARCH BENCH

Objectives. The current topical issues of energy and environmental safety of construction sites and the air-conditioning systems that serve them are identified and analyzed.Method. Using thermal methods and means of controlling heat and power parameters in transitional conditions of energy supply and removal in the system “energy source - energy receiver”, the possibility of identifying its power and flow characteristics that determine and form the processes and modes reflecting the basic quantitative and qualitative levels of current energy transformations.Result. Options have been proposed to solve this problem through the integrated monitoring of some energy-ecological characteristics of the building structures of buildings and structures at the laboratory-experimental research stand “energy source - energy receiver”. The algorithm for identification of thermodynamic forces, flows, properties, changes and reproduction of entropy in the system “energy source - energy receiver”, a functional model and hierarchical representation of a three-level open thermodynamic system “energy source - energy receiver” are presented, some calculated results -experimental determination of the eco-energy characteristics of a fragment of the building envelope by the example of a brick wall.Conclusion. It has been suggested and proved that the experience of joint use of the laws of nonequilibrium and phenomenological thermodynamics for research and modeling of nonequilibrium thermodynamic processes occurring in systems of various kinds, allows you to control their ecological state and increases the accuracy of forecasting costs and rational use of energy resources.

Geometry of Thermodynamic Processes.

Since the 1970s, contact geometry has been recognized as an appropriate framework for the geometric formulation of thermodynamic systems, and in particular their state properties. More recently it has been shown how the symplectization of contact manifolds provides a new vantage point; enabling, among other things, to switch easily between the energy and entropy representations of a thermodynamic system. In the present paper, this is continued towards the global geometric definition of a degenerate Riemannian metric on the homogeneous Lagrangian submanifold describing the state properties, which is overarching the locally-defined metrics of Weinhold and Ruppeiner. Next, a geometric formulation is given of non-equilibrium thermodynamic processes, in terms of Hamiltonian dynamics defined by Hamiltonian functions that are homogeneous of degree one in the co-extensive variables and zero on the homogeneous Lagrangian submanifold. The correspondence between objects in contact geometry and their homogeneous counterparts in symplectic geometry, is extended to the definition of port-thermodynamic systems and the formulation of interconnection ports. The resulting geometric framework is illustrated on a number of simple examples, already indicating its potential for analysis and control.

Numerical studies on the off-design performance of a cryogenic two-phase turbo-expander

The two-phase turbo-expanders are in more popular as their advantage of more provided cooling capacity in cryogenic applications. However, it makes the preliminary or alternative design and off-design prediction for this type turbine to remain an unworked area, due to a lack of better understanding for machine performance under two-phase conditions. This paper numerically studies the machine off-design performance based on a cryogenic turbo-expander, which is a key equipment to supply main cooling capacity for an air separation plant. The investigative off-design conditions including 420 numerical cases cover both superheated region and two-phase region. The simulations of gas expansion involving two-phase flow in nozzle and impeller are performed on non-equilibrium condensation model of ANSYS CFX. According to the state of gas expansion end point, the numerical results could be categorized as three types, i.e. superheated, supercooled and spontaneous condensation expansions. The effect of non-equilibrium thermodynamic process on the outlet parameters also is revealed via comparison with results from ideal equilibrium condensation model. Moreover, the turbo-expander performance maps under superheated and two-phase conditions, including mass flow rate, degree of reaction and total-to-static efficiency, are compared and analyzed. Finally, taking liquid mass fraction as a fundamental parameter as well as velocity ratio, new 3-D performance maps of reaction and efficiency are developed. The research achievements could be applicable to turbine design and performance prediction at two-phase conditions.

Studies on the Exergy Transfer Law for the Irreversible Process in the Waxy Crude Oil Pipeline Transportation.

With the increasing demand of oil products in China, the energy consumption of pipeline operation will continue to rise greatly, as well as the cost of oil transportation. In the field of practical engineering, saving energy, reducing energy consumption and adapting to the international oil situation are the development trends and represent difficult problems. Based on the basic principle of non-equilibrium thermodynamics, this paper derives the field equilibrium equations of non-equilibrium thermodynamic process for pipeline transportation. To seek the bilinear form of “force” and “flow” in the non-equilibrium thermodynamics of entropy generation rate, the oil pipeline exergy balance equation and the exergy transfer pipeline dynamic equation of the irreversibility were established. The exergy balance equation was applied to energy balance evaluation system, which makes the system more perfect. The exergy flow transfer law of the waxy oil pipeline were explored deeply from the directions of dynamic exergy, pressure exergy, thermal exergy and diffusion exergy. Taking an oil pipeline as an example, the influence factors of exergy transfer coefficient and exergy flow density were analyzed separately.