Predicting Ion Sequestration in Charged Polymers with the Steepest-Entropy-Ascent Quantum Thermodynamic Framework.

The steepest-entropy-ascent quantum thermodynamic framework is used to investigate the effectiveness of multi-chain polyethyleneimine-methylenephosphonic acid in sequestering rare-earth ions (Eu3+) from aqueous solutions. The framework applies a thermodynamic equation of motion to a discrete energy eigenstructure to model the binding kinetics of europium ions to reactive sites of the polymer chains. The energy eigenstructure is generated using a non-Markovian Monte Carlo model that estimates energy level degeneracies. The equation of motion is used to determine the occupation probability of each energy level, describing the unique path through thermodynamic state space by which the polymer system sequesters rare-earth ions from solution. A second Monte Carlo simulation is conducted to relate the kinetic path in state space to physical descriptors associated with the polymer, including the radius of gyration, tortuosity, and Eu-neighbor distribution functions. These descriptors are used to visualize the evolution of the polymer during the sequestration process. The fraction of sequestered Eu3+ ions depends upon the total energy of the system, with lower energy resulting in greater sequestration. The kinetics of the overall sequestration are dependent on the steepest-entropy-ascent principle used by the equation of motion to generate a unique kinetic path from an initial non-equilibrium state.

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.

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.

Predicting defect stability and annealing kinetics in two-dimensional PtSe2using steepest entropy ascent quantum thermodynamics.

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework was used to calculate the stability of a collection of point defects in 2D PtSe2and predict the kinetics with which defects rearrange during thermal annealing. The framework provides a non-equilibrium, ensemble-based framework with a self-consistent link between mechanics (both quantum and classical) and thermodynamics. It employs an equation of motion derived from the principle of steepest entropy ascent (maximum entropy production) to predict the time evolution of a set of occupation probabilities that define the states of a system undergoing a non-equilibrium process. The system is described by a degenerate energy landscape of eigenvalues, and the entropy is found from the occupation probabilities and the eigenlevel degeneracies. Scanning tunneling microscopy was used to identify the structure and distribution of point defects observed experimentally in a 2D PtSe2film. A catalog of observed defects includes six unique point defects (vacancies and anti-site defects on Pt and Se sublattices) and twenty combinations of multiple point defects in close proximity. The defect energies were estimated with density functional theory, while the degeneracies, or density of states, for the 2D film with all possible combinations or arrangements of cataloged defects was constructed using a non-Markovian Monte-Carlo approach (i.e. the Replica-Exchange-Wang-Landau algorithm (Vogelet al2013Phys. Rev. Lett.110210603)) with a q-state Potts model. The energy landscape and associated degeneracies were determined for a 2D PtSe2film two molecules thick and30×30unit cells in area (total of 5400 atoms). The SEAQT equation of motion was applied to the energy landscape to determine how an arbitrary density and arrangement of the six defect types evolve during annealing. Two annealing processes were modeled: heating from 77 K (-196 ∘C) to 523 K (250 ∘C) and isothermal annealing at 523 K. The SEAQT framework predicted defect configurations, which were consistent with experimental STM images.

A thermodynamic scaling law for electrically perturbed lipid membranes: Validation with steepest entropy ascent framework.

Experimental evidence has demonstrated the ability of transient pulses of electric fields to alter mammalian cell behavior. Strategies with these pulsed electric fields (PEFs) have been developed for clinical applications in cancer therapeutics, in-vivo decellularization, and tissue regeneration. Successful implementation of these strategies involve understanding how PEFs impact the cellular structures and, hence, cell behavior. The caveat, however, is that the PEF parameter space (i.e., comprising different pulse widths, amplitudes, number of pulses) is large, and design of experiments to explore all possible combinations of pulse parameters is prohibitive from a cost and time standpoint. In this study, a scaling law based on the Ising model is introduced to understand the impact of PEFs on the outer cell lipid membrane so that an understanding developed in one PEF pulse regime may be extended to another. Combining non-Markovian Monte Carlo techniques to determine density-of-states with a novel non-equilibrium thermodynamic framework based on the principle of steepest entropy ascent, the applicability of this scaling model to predict the behavior of both thermally quenched and electrically perturbed lipid membranes is demonstrated. A comparison of the predictions made by the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework to experimental data is performed to validate the robustness of this computational methodology and the resulting scaling law.

Electro-chemo-mechanical model to investigate multi-pulse electric-field-driven integrin clustering.

The effect of pulsed electric fields (PEFs) on transmembrane proteins is not fully understood; how do chemo-mechanical cues in the microenvironment mediate the electric field sensing by these proteins? To answer this key gap in knowledge, we have developed a kinetic Monte Carlo statistical model of the integrin proteins that integrates three components of the morphogenetic field (i.e., chemical, mechanical, and electrical cues). Specifically, the model incorporates the mechanical stiffness of the cell membrane, the ligand density of the extracellular environment, the glycocalyx stiffness, thermal Brownian motion, and electric field induced diffusion. The effects of both steady-state electric fields and transient PEF pulse trains on integrin clustering are studied. Our results reveal that electric-field-driven integrin clustering is mediated by membrane stiffness and ligand density. In addition, we explore the effects of PEF pulse-train parameters (amplitude, polarity, and pulse-width) on integrin clustering. In summary, we demonstrate a computational methodology to incorporate experimental data and simulate integrin clustering when exposed to PEFs for time-scales comparable to experiments (seconds-minutes). Thus, we propose a blueprint for understanding PEF/electric field effects on protein induced signaling and highlight key impediments to incorporating experimental values into computational models such as the kinetic Monte Carlo method.

Low-temperature atomistic spin relaxation and non-equilibrium intensive properties using steepest-entropy-ascent quantum-inspired thermodynamics modeling.

The magnetization of body-centered cubic iron at low temperatures is calculated with the steepest-entropy-ascent quantum thermodynamics (SEAQT) framework. This framework assumes that a thermodynamic property in an isolated system traces the path through state space with the greatest entropy production. Magnetization is calculated from the expected value of a thermodynamic ensemble of quantized spin waves based on the Heisenberg spin model applied to an ensemble of coupled harmonic oscillators. A realistic energy landscape is obtained from a magnon dispersion relation calculated using spin-density-functional-theory. The equilibrium magnetization as well as the evolution of magnetization from a non-equilibrium state to equilibrium are calculated from the path of steepest entropy ascent determined from the SEAQT equation of motion in state space. The framework makes it possible to model the temperature and time-dependence of magnetization without a detailed description of magnetic damping. The approach is also used to define intensive properties (temperature and magnetic field strength) that are fundamentally, i.e. canonically or grand canonically, valid for any non-equilibrium state. Given the assumed magnon dispersion relation, the SEAQT framework is used to calculate the equilibrium magnetization at different temperatures and external magnetic fields and the results are shown to closely agree with experiment for temperatures less than 500 K. The time-dependent evolution of magnetization from different initial states and interactions with a reservoir is also predicted.

Predicting continuous and discontinuous phase decompositions using steepest-entropy-ascent quantum thermodynamics.

The decomposition kinetics of a solid solution into separate phases are analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. This equation and the steepest-entropy-ascent quantum thermodynamic framework of which it is a part make it possible to track kinetic processes in systems at nonequilibrium while retaining the framework of classical equilibrium thermodynamics. The general equation of motion is particularized for the case of the decomposition of a binary alloy, and a solution model is used to build an approximate energy eigenstructure, or pseudoeigenstructure, for the alloy system. This equation is then solved with the pseudoeigenstructure to obtain a unique reaction path and the decomposition kinetics of the alloy. For a hypothetical solid solution with a miscibility gap at low temperatures, the conditions under which this framework predicts a continuous transformation path (spinodal decomposition) or a discontinuous one (nucleation and growth) are demonstrated.

CH4 Adsorption Probability on GaN(0001) and (000-1) during Metalorganic Vapor Phase Epitaxy and Its Relationship to Carbon Contamination in the Films.

Suppression of carbon contamination in GaN films grown using metalorganic vapor phase epitaxy (MOVPE) is a crucial issue in its application to high power and high frequency electronic devices. To know how to reduce the C concentration in the films, a sequential analysis based on first principles calculations is performed. Thus, surface reconstruction and the adsorption of the CH4 produced by the decomposition of the Ga source, Ga(CH3)3, and its incorporation into the GaN sub-surface layers are investigated. In this sequential analysis, the dataset of the adsorption probability of CH4 on reconstructed surfaces is indispensable, as is the energy of the C impurity in the GaN sub-surface layers. The C adsorption probability is obtained based on steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic ensemble-based, non-phenomenological framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium. This framework is suitable especially when one studies the adsorption behavior of an impurity molecule because the conventional approach, the chemical potential control method, cannot be applied to a quantitative analysis for such a system. The proposed sequential model successfully explains the influence of the growth orientation, GaN(0001) and (000-1), on the incorporation of C into the film. This model can contribute to the suppression of the C contamination in GaN MOVPE.

A method for predicting non-equilibrium thermal expansion using steepest-entropy-ascent quantum thermodynamics.

Steepest-entropy-ascent quantum thermodynamics (SEAQT) is an intriguing approach that describes equilibrium and dynamic processes in a self-consistent way. To date, it has been applied primarily to gas phase systems because of the difficulty in generating the complex eigenstructures (eigenvalues and eigenfunctions) associated with solid or liquid phases. In this contribution, the SEAQT modeling is extended to the solid phase by constructing a so-called pseudo-eigenstructure, and its applicability is demonstrated by calculating the thermal expansion of metallic silver for three cases: (a) stable equilibrium, (b) along three irreversible paths from different initial non-equilibrium states to stable equilibrium, and (c) along an irreversible path between two stable equilibrium states. The SEAQT framework with an anharmonic pseudo-eigenstructure predicts reasonable values for the equilibrium thermal expansion. For the irreversible cases considered, the SEAQT approach makes it possible to predict the time-dependence of lattice relaxations from the initial state to the final equilibrium state.

Influence of Pulsed Electric Fields and Mitochondria-Cytoskeleton Interactions on Cell Respiration.

Pulsed electric fields with microsecond pulse width (µsPEFs) are used clinically; namely, irreversible electroporation/Nanoknife is used for soft tissue tumor ablation. The µsPEF pulse parameters used in irreversible electroporation (0.5-1 kV/cm, 80-100 pulses, ∼100 µs each, 1 Hz frequency) may cause an internal field to develop within the cell because of the disruption of the outer cell membrane and subsequent penetration of the electric field. An internal field may disrupt voltage-sensitive mitochondria, although the research literature has been relatively unclear regarding whether such disruptions occur with µsPEFs. This investigation reports the influence of clinically used µsPEF parameters on mitochondrial respiration in live cells. Using a high-throughput Agilent Seahorse machine, it was observed that µsPEF exposure comprising 80 pulses with amplitudes of 600 or 700 V/cm did not alter mitochondrial respiration in 4T1 cells measured after overnight postexposure recovery. To record alterations in mitochondrial function immediately after µsPEF exposure, high-resolution respirometry was used to measure the electron transport chain state via responses to glutamate-malate and ADP and mitochondrial membrane potential via response to carbonyl cyanide-p-trifluoromethoxyphenylhydrazone. In addition to measuring immediate mitochondrial responses to µsPEF exposure, measurements were also made on cells permeabilized using digitonin and those with compromised cytoskeleton due to actin depolymerization via treatment with the drug latrunculin B. The former treatment was used as a control to tease out the effects of plasma membrane permeabilization, whereas the latter was used to investigate indirect effects on the mitochondria that may occur if µsPEFs impact the cytoskeleton on which the mitochondria are anchored. Based on the results, it was concluded that within the pulse parameters tested, µsPEFs alone do not hinder mitochondrial physiology but can be used to impact the mitochondria upon compromising the actin. Mitochondrial susceptibility to µsPEF after actin depolymerization provides, to our knowledge, a novel avenue for cancer therapeutics.

Ab initio relaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework.

Quantum systems driven by time-dependent Hamiltonians are considered here within the framework of steepest-entropy-ascent quantum thermodynamics (SEAQT) and used to study the thermodynamic characteristics of such systems. In doing so, a generalization of the SEAQT framework valid for all such systems is provided, leading to the development of an ab initio physically relevant expression for the intrarelaxation time, an important element of this framework and one that had as of yet not been uniquely determined as an integral part of the theory. The resulting expression for the relaxation time is valid as well for time-independent Hamiltonians as a special case and makes the description provided by the SEAQT framework more robust at the fundamental level. In addition, the SEAQT framework is used to help resolve a fundamental issue of thermodynamics in the quantum domain, namely, that concerning the unique definition of process-dependent work and heat functions. The developments presented lead to the conclusion that this framework is not just an alternative approach to thermodynamics in the quantum domain but instead one that uniquely sheds new light on various fundamental but as of yet not completely resolved questions of thermodynamics.

Modeling the Non-Equilibrium Process of the Chemical Adsorption of Ammonia on GaN(0001) Reconstructed Surfaces Based on Steepest-Entropy-Ascent Quantum Thermodynamics.

Clearly understanding elementary growth processes that depend on surface reconstruction is essential to controlling vapor-phase epitaxy more precisely. In this study, ammonia chemical adsorption on GaN(0001) reconstructed surfaces under metalorganic vapor phase epitaxy (MOVPE) conditions (3Ga-H and Nad-H + Ga-H on a 2 × 2 unit cell) is investigated using steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic-ensemble based, first-principles framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium where the state evolution is a combination of reversible and irreversible dynamics. SEAQT is an ideal choice to handle this problem on a first-principles basis since the chemical adsorption process starts from a highly non-equilibrium state. A result of the analysis shows that the probability of adsorption on 3Ga-H is significantly higher than that on Nad-H + Ga-H. Additionally, the growth temperature dependence of these adsorption probabilities and the temperature increase due to the heat of reaction is determined. The non-equilibrium thermodynamic modeling applied can lead to better control of the MOVPE process through the selection of preferable reconstructed surfaces. The modeling also demonstrates the efficacy of DFT-SEAQT coupling for determining detailed non-equilibrium process characteristics with a much smaller computational burden than would be entailed with mechanics-based, microscopic-mesoscopic approaches.

Generalized thermodynamic relations for a system experiencing heat and mass diffusion in the far-from-equilibrium realm based on steepest entropy ascent.

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micromechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and near-equilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single-particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in the near-equilibrium realm.

Steepest-entropy-ascent quantum thermodynamic modeling of the relaxation process of isolated chemically reactive systems using density of states and the concept of hypoequilibrium state.

This paper presents a study of the nonequilibrium relaxation process of chemically reactive systems using steepest-entropy-ascent quantum thermodynamics (SEAQT). The trajectory of the chemical reaction, i.e., the accessible intermediate states, is predicted and discussed. The prediction is made using a thermodynamic-ensemble approach, which does not require detailed information about the particle mechanics involved (e.g., the collision of particles). Instead, modeling the kinetics and dynamics of the relaxation process is based on the principle of steepest-entropy ascent (SEA) or maximum-entropy production, which suggests a constrained gradient dynamics in state space. The SEAQT framework is based on general definitions for energy and entropy and at least theoretically enables the prediction of the nonequilibrium relaxation of system state at all temporal and spatial scales. However, to make this not just theoretically but computationally possible, the concept of density of states is introduced to simplify the application of the relaxation model, which in effect extends the application of the SEAQT framework even to infinite energy eigenlevel systems. The energy eigenstructure of the reactive system considered here consists of an extremely large number of such levels (on the order of 10^{130}) and yields to the quasicontinuous assumption. The principle of SEA results in a unique trajectory of system thermodynamic state evolution in Hilbert space in the nonequilibrium realm, even far from equilibrium. To describe this trajectory, the concepts of subsystem hypoequilibrium state and temperature are introduced and used to characterize each system-level, nonequilibrium state. This definition of temperature is fundamental rather than phenomenological and is a generalization of the temperature defined at stable equilibrium. In addition, to deal with the large number of energy eigenlevels, the equation of motion is formulated on the basis of the density of states and a set of associated degeneracies. Their significance for the nonequilibrium evolution of system state is discussed. For the application presented, the numerical method used is described and is based on the density of states, which is specifically developed to solve the SEAQT equation of motion. Results for different kinds of initial nonequilibrium conditions, i.e., those for gamma and Maxwellian distributions, are studied. The advantage of the concept of hypoequilibrium state in studying nonequilibrium trajectories is discussed.