Nonequilibrium Path Research Articles

Microstructure and wear resistance of laser cladding a novel nickel-based alloy coating

A novel crack-free nickel-based alloy coating was successfully fabricated using laser cladding. By utilizing the TCNI (v10) commercial multi-component database of nickel-based superalloys, the equilibrium phase diagram and non-equilibrium solidification path of this novel alloy were revealed using the CALPHAD method. The substrate phase of the NiCrFeWBSiMo-CeO2 coating consists of the face centered cubic (FCC) phase, along with several strengthening phases. The coating exhibits a microhardness of ∼575 HV, while the coefficient of friction (COF) and volume wear rate measure at 0.39 and 1.1 mg respectively, indicating excellent wear resistance.

Predicting Polymer Brush Behavior in Solvents Using the Steepest-Entropy-Ascent Quantum Thermodynamic Framework.

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is utilized to study the effects of temperature on polymer brushes. The brushes are represented by a discrete energy spectrum, and energy degeneracies obtained through the replica-exchange Wang-Landau algorithm. The SEAQT equation of motion is applied to the density of states to establish a unique kinetic path from an initial thermodynamic state to a stable equilibrium state. The kinetic path describes the brush's evolution in state space, as it interacts with a thermal reservoir. The predicted occupation probabilities along the kinetic path are used to determine the expected thermodynamic and structural properties. The polymer density profile of a polystyrene brush in cyclohexane solvent is predicted using the equation of motion, and it agrees qualitatively with the experimental density profiles. The Flory-Huggins parameter chosen to describe brush-solvent interactions affects the solvent distribution in the brush but has a minimal impact on the polymer density profile. Three types of nonequilibrium kinetic paths with differing amounts of entropy production are considered: a heating path, a cooling path, and a heating-cooling path. Properties such as tortuosity, radius of gyration, brush density, solvent density, and brush chain conformations are calculated for each path.

Incorporating dynamic recrystallization into a crystal plasticity model for high-temperature deformation of Ti-6Al-4V

During hot deformation of (α+β) titanium alloys, the simultaneous action of strain and temperature in the (α+β) regime facilitates dynamic recovery, dynamic recrystallization (DRX), and phase transformations via non-equilibrium paths. DRX is manifested in the form of fine recrystallized α or β grains. In the present study, a two-phase crystal plasticity finite element framework (CP-DRX) has been developed which incorporates DRX kinetics into the crystal plasticity (CP) model to predict the flow characteristics of Ti-6Al-4V alloys during thermo-mechanical processing. The CP slip system parameters, as well as elastic properties from both α and β phases of Ti, are calibrated for different strain rate conditions. An EBSD-informed two-phase microstructure representation has been utilized in the CP-DRX framework to explore the time-dependent evolution of DRX microstructure and crystal orientation for different strain rate conditions. The proposed CP-DRX can capture the evolution of crystal orientation and plastic flow stress–strain response of polycrystalline Ti-6Al-4V during the deformation process. Furthermore, the proposed model is able to capture the softening behavior, observed in average stress–strain response from experiments performed using a Gleeble thermomechanical simulator and predict the recrystallization texture.

Predicting non-equilibrium folding behavior of polymer chains using the steepest-entropy-ascent quantum thermodynamic framework.

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is used to explore the influence of heating and cooling on polymer chain folding kinetics. The framework predicts how a chain moves from an initial non-equilibrium state to stable equilibrium along a unique thermodynamic path. The thermodynamic state is expressed by occupation probabilities corresponding to the levels of a discrete energy landscape. The landscape is generated using the Replica Exchange Wang-Landau method applied to a polymer chain represented by a sequence of hydrophobic and polar monomers with a simple hydrophobic-polar amino acid model. The chain conformation evolves as energy shifts among the levels of the energy landscape according to the principle of steepest entropy ascent. This principle is implemented via the SEAQT equation of motion. The SEAQT framework has the benefit of providing insight into structural properties under non-equilibrium conditions. Chain conformations during heating and cooling change continuously without sharp transitions in morphology. The changes are more drastic along non-equilibrium paths than along quasi-equilibrium paths. The SEAQT-predicted kinetics are fitted to rates associated with the experimental intensity profiles of cytochrome c protein folding with Rouse dynamics.

Optimizing dynamical functions for speed with stochastic paths.

Living systems are built from microscopic components that function dynamically; they generate work with molecular motors, assemble and disassemble structures such as microtubules, keep time with circadian clocks, and catalyze the replication of DNA. How do we implement these functions in synthetic nanostructured materials to execute them before the onset of dissipative losses? Answering this question requires a quantitative understanding of when we can improve performance and speed while minimizing the dissipative losses associated with operating in a fluctuating environment. Here, we show that there are four modalities for optimizing dynamical functions that can guide the design of nanoscale systems. We analyze Markov models that span the design space: a clock, ratchet, replicator, and self-assembling system. Using stochastic thermodynamics and an exact expression for path probabilities, we classify these models of dynamical functions based on the correlation of speed with dissipation and with the chosen performance metric. We also analyze random networks to identify the model features that affect their classification and the optimization of their functionality. Overall, our results show that the possible nonequilibrium paths can determine our ability to optimize the performance of dynamical functions, despite ever-present dissipation, when there is a need for speed.

Stochastic paths controlling speed and dissipation.

Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.

Influence of dynamic compression on the phase transition of cyclohexane

Alkanes are an important part of petroleum, and the phase structure and stability of alkanes in the deep earth are of great significance for petroleum exploitation. In this work, we performed Raman spectroscopy of cyclohexane under static and dynamic pressures at room temperature. Cyclohexane underwent four solid–solid transitions near 0.66, 1.57, 3.39 and 13.59 GPa during static compression up to 25 GPa. Under dynamic compression, two new phases Ⅳ' and Ⅴ' of cyclohexane were found at 2.23 GPa and 3.98 GPa, respectively, as the pressure increased from 0.91 GPa to 2.23, 3.98, 5.65, 6.80 and 7.45 GPa step by step within 5 ms. At a higher compression rate, cyclohexane turned from phase Ⅳ into phase Ⅵ' as the pressure increased from 2.77 to 20.74 GPa within 5 ms. The Raman results show that the cyclohexane molecule forms a geometric structure with low symmetry under dynamic pressure. We speculated that dynamic compression provides a high-pressure and temperature nonequilibrium path for cyclohexane, which could compel molecules to adjust and rearrange to form new phases.

Universal Criteria for Single Femtosecond Pulse Ultrafast Magnetization Switching in Ferrimagnets.

Single-pulse switching has been experimentally demonstrated in ferrimagnetic GdFeCo and Mn_{2}Ru_{x}Ga alloys. Complete understanding of single-pulse switching is missing due to the lack of an established theory accurately describing the transition to the nonequilibrium reversal path induced by femtosecond laser photoexcitation. In this work, we present general macroscopic theory for the magnetization dynamics of ferrimagnetic materials upon femtosecond laser excitation. Our theory reproduces quantitatively all stages of the switching process observed in experiments. We directly compare our theory to computer simulations using atomistic spin dynamics methods for both GdFeCo and Mn_{2}Ru_{x}Ga alloys. We provide explicit expressions for the magnetization relaxation rates in terms of microscopic parameters, which allows us to propose universal criteria for switching in ferrimagnets.

Microscopic theory of ionic motion in solids

Drag and diffusion of mobile ions in solids are of interest for both purely theoretical and applied scientific communities. This article proposes a theoretical description of ion drag in solids that can be used to estimate ionic conductivities in crystals, and forms a basis for the rational design of solid electrolyte materials. Starting with a general solid-state Hamiltonian, we employ the nonequilibrium path integral formalism to develop a microscopic theory of ionic transport in solids in the presence of thermal fluctuations. As required by the fluctuation-dissipation theorem, we obtain a relation between the variance of the random force and friction. Because of the crystalline nature of the system, however, the two quantities are tensorial. We use the drag tensor to write down the formula for ionic mobility, determined by the potential profile generated by the crystal's ions.

Study on non-equilibrium solidification microstructure of Al–Cu3–Si–Mg alloy by MMDF

Al–Cu3–Si–Mg wheel hubs were prepared by molten metals die forging (MMDF). The as-cast microstructure morphology of the alloy formed under pressure was observed by optical microscope and scanning electron microscope. The granular phases θ (Al2Cu) were distributed in the α–Al grains, and the cross phases β (Mg2Si) grew near the grain boundary in the α–Al grains. Polygonal compounds φ (AlxTi9La2Ce6Cu) and irregular eutectic structures mainly formed by (α + Al2Cu) eutectic formed under non-equilibrium solidification were found at the grain boundaries. Q (Al5Cu2Mg8Si6) phases were found at the intersection of grain boundaries. With the increase of pressure, the proportion of irregular eutectic structures (α + Al2Cu) decreased from 7.3% to 5.2%. Combined with microstructure analysis and thermodynamic software analysis, the non-equilibrium solidification path was determined as follows: L → L + φ → L + α + φ → L + (α + e) + α + φ → (α + e) + Q + α + φ → (α + e) + Q + [α + θ] + φ → (α + e) + Q + [α + θ + β] + φ

First Principle Calculation and Thermodynamic Analysis of Coexisting Phase of Cu-Cr-Sn Copper Alloy

Based on the idea of material genetic engineering, according to the innovative design of the whole material chain and taking high-strength and high conductivity copper alloy as the research object and carrier, this paper carries out high-throughput integrated calculation and design methods such as alloy characteristic microstructure, interface chemistry, thermodynamics and kinetics, establishes the prediction model of material composition structure process performance relationship, and realizes the high-throughput preparation and characterization technology of materials, Form a low-cost and rapid development capability oriented by application objectives. In this paper, the mixed matrix and characteristic microstructure sequence are optimized by high-throughput calculation, the thermodynamic and kinetic conditions of material preparation and synthesis are analyzed, and the phase diagram and solidification technology are calculated by CALPHAD to optimize the content, morphology and distribution of characteristic microstructure in the alloy. By designing polycrystalline and peritectic platforms, the microstructure type, morphology and content of characteristic microstructure can be controlled. At the same time, the type, content and distribution of the second phase are regulated by multi-element alloy equilibrium calculation phase diagram and non-equilibrium solidification path calculation, so as to realize the integrated calculation of materials and the selection of composition and process sequence range.

The unique limit cycle in post Keynesian theory

This paper establishes not only the existence and uniqueness of a limit cycle (representing persistent growth cycles) but also the convergence of every non-equilibrium solution path (describing the state of the economy) to the unique limit cycle in post Keynesian theory.

Probability distribution for heat exchange in plastic deformation.

Fluctuation theorems allow one to obtain equilibrium information from nonequilibrium experiments. The probability distribution function of the relevant magnitude measured along the irreversible nonequilibrium trajectories is an essential ingredient of fluctuation theorems. In small systems, where fluctuations can be larger than average values, probability distribution functions often deviate from being Gaussian, showing long tails, mostly exponential, and usually strongly asymmetric. Recently, the probability distribution function of the van Hove correlation function of the relevant magnitude was calculated, instead of that of the magnitude itself. The resulting probability distribution function is highly symmetric, obscuring the application of fluctuation theorems. Here, the discussion is illustrated with the help of results for the heat exchanged during plastic deformation of aluminum nanowires, obtained from molecular dynamics calculations. We find that the probability distribution function for the heat exchanged is centrally Gaussian, with asymmetric exponential tails further out. By calculating the symmetry function we show that this distribution is consistent with fluctuation theorems relating the differences between two equilibrium states to an infinite number of nonequilibrium paths connecting those two states.

Phase transformations and thermal conductivity of the In-Ag alloys

Phase transformations and thermal conductivity of three In-Ag alloys with 5, 15, and 45 wt.% of Ag were experimentally investigated in the present work. Phase transition temperatures were measured using differential scanning calorimetry (DSC). DSC heating scans were compared with the equilibrium and non-equilibrium solidification paths, calculated by using optimized thermodynamic parameters from literature and calculation of phase diagrams (CALPHAD) method. The flash method was employed for the determination of thermal diffusivity and thermal conductivity of the investigated alloys in the temperature range from 25 to 100 °C. It has been found that an increase in silver content does not lead to an increase in the thermal conductivity of the investigated alloys. Thermal conductivities for all three investigated In-Ag alloys slightly decrease with temperature increasing.

Discrete-time construction of nonequilibrium path integrals on the Kostantinov–Perel’ time contour

Rigorous nonequilibrium actions for the many-body problem are usually derived by means of path integrals combined with a discrete temporal mesh on the Schwinger–Keldysh time contour. The latter suffers from a fundamental limitation: the initial state on this contour cannot be arbitrary, but necessarily needs to be described by a non-interacting density matrix, while interactions are switched on adiabatically. The Kostantinov–Perel’ contour overcomes these and other limitations, allowing generic initial-state preparations. In this article, we apply the technique of the discrete temporal mesh to rigorously build the nonequilibrium path integral on the Kostantinov–Perel’ time contour.

Fluctuation theorem with two independent field parameters: The one-dimensional compressible Ising model.

In this work we consider the nonequilibrium mechanical and magnetic work performed on a one-dimensional compressible Ising model. In the harmonic approximation we easily integrate the mechanical degrees of freedom of the model, and the resulting effective Hamiltonian depends on two external parameters, the magnetic field and the force applied along the chain. As the model is exactly soluble in one dimension we can determine the free energy difference between two arbitrary thermodynamic states of the system. We show the validity of the Jarzynski equality, which relates the free energy difference between two thermodynamic states of the system and the average work performed by external agents in a finite time, through nonequilibrium paths between the same thermodynamic states. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field and the mechanical force applied to the system.

Testing ground for fluctuation theorems: The one-dimensional Ising model.

In this paper we determine the nonequilibrium magnetic work performed on a Ising model and relate it to the fluctuation theorem derived some years ago by Jarzynski. The basic idea behind this theorem is the relationship connecting the free energy difference between two thermodynamic states of a system and the average work performed by an external agent, in a finite time, through nonequilibrium paths between the same thermodynamic states. We test the validity of this theorem by considering the one-dimensional Ising model where the free energy is exactly determined as a function of temperature and magnetic field. We have found that the Jarzynski theorem remains valid for all the values of the rate of variation of the magnetic field applied to the system. We have also determined the probability distribution function for the work performed on the system for the forward and reverse processes and verified that predictions based on the Crooks relation are equally correct. We also propose a method to calculate the lag between the current state of the system and that of the equilibrium based on macroscopic variables. We have shown that the lag increases with the sweeping rate of the field at its final value for the reverse process, while it decreases in the case of the forward process. The lag increases linearly with the size of the chain and with a slope decreasing with the inverse of the rate of variation of the field.

Non-equilibrium solidification and microsegregation in centrifugally cast high speed steel for rolls

When regarding as-cast microstructures of highly alloyed metals, microsegregation of alloying elements is a common feature resulting from non-equilibrium conditions during solidification. The aim of this work is to predict the occurrence and severity of microsegregation in highly alloyed, centrifugally cast high speed steel used for rolls. The prediction was performed using thermodynamic Scheil-Gulliver modelling with Thermo-Calc software. The modelled predictions were then compared with differential scanning calorimetry, X-ray diffraction, light and electron microscopy with energy dispersive spectroscopy, all performed on an as-cast roll shell. Results show that chromium, molybdenum and vanadium have the highest tendency to microsegregation. Vanadium tends to form negative microsegregation, while molybdenum and chromium form positive microsegregation. Scanning electron microscopy revealed the presence of complex eutectic carbides, confirming the Scheil-Gulliver non-equilibrium solidification path via two main successive eutectic reactions.

Non-equilibrium Annealed Damage Phenomena: A Path Integral Approach

We investigate the applicability of the path integral of non-equilibrium statistical mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle model with a thermal noise and a fiber-bundle model with a decay of fibers are considered. Initially, we develop an analogy with the Gibbs formalism of non-equilibrium states. Later, we switch from the approach of non-equilibrium states to the approach of non-equilibrium paths. Behavior of path fluctuations in the system is described in terms of effective temperature parameters. An equation of path as an analogue of the equation of state and a law of path-balance as an analogue of the law of conservation of energy are developed. Also, a formalism of a free energy potential is developed. For fluctuations of paths in the system, the statistical distribution is found to be Gaussian. Also, we find the ‘true’ order parameters linearizing the matrix of fluctuations. The last question we discuss is the applicability of the phase transition theory to non-equilibrium processes. From near-equilibrium processes to stationary processes (dissipative structures), and then to significantly non-equilibrium processes: Through these steps we generalize the concept of a non-equilibrium phase transition.

Nonequilibrium work theorems applied to transitions between configurational domains

A nonequilibrium simulation scheme extending the field of applicability of the Jarzynski equality (Jarzynski 1997 Phys. Rev. Lett. 78 2690) and Crooks fluctuation theorem (Crooks 2000 Phys. Rev. E 61 2361) is presented. The algorithm is based on steps, consisting of transition kernels, alternated to relaxation kernels, that drive the system from an initial to a final configurational domain within the space of the (externally controlled) collective coordinates. This allows the producing of nonequilibrium paths connecting two states with arbitrary shape and size in the space of the collective coordinates, giving access to their free energy difference. The method can be viewed as a generalization of the steered molecular dynamics, a technique commonly applied in simulation to calculate the potentials of mean force along an established monodimensional path in the space of the collective coordinates. A numerical validation of the method is provided by estimating the free energy differences in two model systems featured by a double-well potential. The outcomes are compared to those obtained from standard steered molecular dynamics simulations.