Nonequilibrium Research Articles

Nonequilibrium thermodynamics of non-ideal reaction-diffusion systems: Implications for active self-organization.

We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena, such as liquid-liquid phase separation, coacervation, and the formation of biomolecular condensates.

Playing with active matter

In the past 20 years, active matter has been a very successful research field, bridging the fundamental physics of nonequilibrium thermodynamics with applications in robotics, biology, and medicine. Active particles, contrary to Brownian particles, can harness energy to generate complex motions and emerging behaviors. Most active-matter experiments are performed with microscopic particles and require advanced microfabrication and microscopy techniques. Here, we propose some macroscopic experiments with active matter employing commercially available toy robots (the Hexbugs). We show how they can be easily modified to perform regular and chiral active Brownian motion and demonstrate through experiments fundamental signatures of active systems such as how energy and momentum are harvested from an active bath, how obstacles can sort active particles by chirality, and how active fluctuations induce attraction between planar objects (a Casimir-like effect). These demonstrations enable hands-on experimentation with active matter and showcase widely used analysis methods.

Numerical simulation of phase transition with the hyperbolic Godunov-Peshkov-Romenski model

In this paper, a thermodynamically consistent numerical solution of the interfacial Riemann problem for the first-order hyperbolic continuum model of Godunov, Peshkov and Romenski (GPR model) is presented. In the presence of phase transition, interfacial physics are governed by molecular interaction on a microscopic scale, beyond the scope of the macroscopic continuum model in the bulk phases. The developed approximate two-phase Riemann solvers tackle this multi-scale problem, by incorporating a local thermodynamic model to predict the interfacial entropy production. Using phenomenological relations of non-equilibrium thermodynamics, interfacial mass and heat fluxes are derived from the entropy production and provide closure at the phase boundary. We employ the proposed Riemann solvers in an efficient sharp interface level-set Ghost-Fluid framework to provide coupling conditions at phase interfaces under phase transition. As a single-phase benchmark, a Rayleigh-Bénard convection is studied to compare the hyperbolic thermal relaxation formulation of the GPR model against the hyperbolic-parabolic Euler-Fourier system. The novel interfacial Riemann solvers are validated against molecular dynamics simulations of evaporating shock tubes with the Lennard-Jones shifted and truncated potential. On a macroscopic scale, evaporating shock tubes are computed for the material n-Dodecane and compared against Euler-Fourier results. Finally, the efficiency and robustness of the scheme is demonstrated with shock-droplet interaction simulations that involve both phase transfer and surface tension, while featuring severe interface deformations.

Efficient training of energy-based models using Jarzynski equality**This article is an updated version of: Carbone D, Hua M, Coste S and Vanden-Eijnden E 2023 Efficient training of energy-based models using Jarzynski equality Advances in Neural Information Processing Systems vol 36, ed A Oh, T Naumann, A Globerson, K Saenko, M Hardt and S Levine (Curran Associates, Inc.) pp 52583–614.

Abstract Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is well measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is, however, challenging because the computation of its gradient with respect to the model parameters requires sampling of the model distribution. Here, we show how the results for nonequilibrium thermodynamics based on the Jarzynski equality together with tools from sequential Monte Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA), in which each walker acquires a weight that enables the estimation of the gradient of the CE at any step during gradient descent, thereby bypassing sampling biases induced by slow mixing of the ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST and CIFAR-10 datasets. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.

Research on Non-Equilibrium Dynamics Theory in Chemical Thermodynamics

Non-equilibrium dynamics theory is an important branch of chemical thermodynamics, widely applied in describing complex chemical reaction systems far from equilibrium. With the advancement of modern science and technology, an increasing number of chemical reactions exhibit unique behaviors under non-equilibrium conditions, such as self-organization and periodic oscillations—nonlinear phenomena. This paper systematically explores the distinctions between non-equilibrium and equilibrium states, introduces the fundamental principles of non-equilibrium thermodynamics, and analyzes cutting-edge issues such as nonlinear phenomena and multi-scale dynamics. Additionally, it discusses the specific applications of non-equilibrium dynamics in far-from-equilibrium reactions, heterogeneous catalysis, and industrial chemical processes, addressing both theoretical and experimental challenges. Through the combination of theoretical analysis and practical application, this paper aims to provide new insights and methodologies for research on non-equilibrium dynamics in the field of chemistry.

A thermodynamic framework for nonequilibrium self-assembly and force morphology tradeoffs in branched actin networks.

Branched actin networks are involved in a variety of cellular processes, most notably the formation of lamellipodia in the leading edge of the cell. These systems adapt to varying loads through force dependent assembly rates that allow the network density and material properties to be modulated. Recent experimental work has described growth and force feedback mechanisms in these systems. Here, we consider the role played by energy dissipation in determining the kind of growth-force-morphology curves obtained in experiments. We construct a minimal model of the branched actin network self assembly process incorporating some of the established mechanisms. Our minimal analytically tractable model is able to reproduce experimental trends in density and growth rate. Further, we show how these trends depend crucially on entropy dissipation and change quantitatively if the entropy dissipation is parametrically set to values corresponding to a quasistatic state. Finally, we also identify the potential energy costs of adaptive behavior by branched actin networks, using insights from our minimal models. We suggest that the dissipative cost in the system beyond what is necessary to move the load may be necessary to maintain an adaptive steady state. Our results hence show how constraints from stochastic thermodynamics and non-equilibrium thermodynamics may bound or constrain the structures that result in such force generating processes.

Biothermodynamic analysis of the Dengue virus: Empirical formulas, biosynthesis reactions and thermodynamic properties of antigen-receptor binding and biosynthesis

After the experience with the COVID-19 pandemic, WHO has issued a warning about the possible causes of future pandemics. One such causative agent is the Dengue virus. Until now, we have had information mostly on biological properties of the Dengue virus and very little information about its chemical and thermodynamic properties. To be better prepared for a potential Dengue pandemic, the goal of this paper is to chemically and thermodynamically characterize the Dengue virus, as well as to describe the biophysical basis of the virus-host interactions of the Dengue virus. To that goal, the empirical formula was determined, as well as biosynthesis reactions and thermodynamic properties of antigen-receptor binding and thermodynamic properties of biosynthesis and multiplication of the Dengue virus. A model was developed of virus-host interactions between the Dengue virus and its host tissues, based on nonequilibrium thermodynamics.

Non-equilibrium thermodynamics in NMR: understanding quadrupolar spin-1 systems.

In this study, we explore the non-equilibrium thermodynamics of a quantum system,
specifically focusing on spin-1 quadrupole nuclei. By employing fundamental principles
from quantum mechanics and statistical mechanics, we aim to understand the behavior
of the quadrupole spin-1 nuclei when subjected to external perturbations. Our analysis
involves the investigation of the system's dynamic response to non-equilibrium conditions through the manipulation of a work parameter. By treating work as a random
variable, we gather data from multiple cycles of finite duration, enabling us to compute
the complete distribution of the work generated during this process. Through these
finite-time non-equilibrium process data, we are able to determine equilibrium values
for important quantities such as the difference in free energy between the initial and
final states of the system. Additionally, we explore various properties of the system's
work distribution.

Thermodynamics of the Quantum Mpemba Effect.

We investigate the quantum Mpemba effect from the perspective of nonequilibrium quantum thermodynamics by studying relaxation dynamics of quantum systems coupled to a Markovian heat bath, which are described by Davies maps. Starting from a state with coherences in the energy eigenbasis, we demonstrate that an exponential speedup to equilibrium will always occur if the state is transformed to a diagonal state in the energy eigenbasis, provided that the spectral gap of the generator is defined by a complex eigenvalue. When the transformed state has a higher nonequilibrium free energy, we argue using thermodynamic reasoning that this is a genuine quantum Mpemba effect. Furthermore, we show how a unitary transformation on an initial state can always be constructed to yield the effect and demonstrate our findings by studying the dynamics of both the nonequilibrium free energy and the irreversible entropy production in single and multiqubit examples.

Theory of wetting dynamics with surface binding

Abstract Biomolecules, such as proteins and nucleic acids, can phase separate in the cytoplasm of cells to form biomolecular condensates. Such condensates are often liquid-like droplets that can wet biological surfaces such as membranes. Many molecules that participate in phase separation can also reversibly bind to membrane surfaces. When a droplet wets a surface, molecules can diffuse inside and outside of the droplet or in the bound state on the surface. How the interplay between surface binding, diffusion in surface and bulk affects the wetting kinetics is not well understood. Here, we derive the governing equations using non-equilibrium thermodynamics by relating the thermodynamic fluxes and forces at the surface coupled to the bulk. We study the spreading dynamics in the presence of surface binding and find that binding speeds up wetting by nucleating a droplet inside the surface. Our results suggest that the wetting dynamics of droplets can be regulated by two-dimensional surface droplets in the surface-bound layer through changing the binding affinity to the surfaces. These findings are relevant both to engineering life-like systems with condensates and vesicles, and biomolecular condensates in living cells.

‘IT FROM BIT’: How does information shape the structures in the Universe?

Based on a synthesis of three main ingredients: (i) the Shannon information in non-equilibrium systems, (ii) the semiclassical energy-time quantization rule and (iii) the quasi-static information-energy correspondence, a new general rule for the quantization of quasi-static information states supported by an environment away from equilibrium is introduced if the history of the environment is known as a function of time in terms of its thermodynamic potential for information T ( t ) Δ S ( t ) that is a free energy measuring the distance from equilibrium Δ S ( t ) , and T ( t ) is the mean temperature of the environment at time t . This all new quasi-static information-time quantization rule is applied to the expanding Universe using a phenomenological thermodynamic potential for information in the matter-dominated era in order to find the eigen-information of the persistent structures that are supported by the universe (or the local environments therein) at any given epoch, thus providing an information–theoretic foundation for formation of structures and rise of complexity with time that embodies the cosmic evolution as epitomized by the late Wheeler’s famous conjecture ‘it from bit’. This theoretical procedure must also open new avenues for further research into the quantum theory of information and complexity in non-equilibrium thermodynamics.

Co-sorption of volatile components in polymer-based pharmaceutical formulations

Amorphous Solid Dispersions (ASDs) are mixtures of active pharmaceutical ingredients (APIs) and polymers aiming to increase API aqueous solubility and bioavailability. ASDs are often produced using solvent-based manufacturing, such as spray drying. Due to solubility or miscibility limitations in one solvent, solvent mixtures are frequently used for this purpose. Drying solvents or solvent mixtures from polymer-based products like ASDs is an energy-intensive and time-consuming process. Designing and optimising this drying process requires knowledge of the sorption isotherms of the solvent(s) in these polymer-based products. In this work, we developed a novel approach for measuring the simultaneous absorption/desorption of two solvents in a polymer. Combining classical dynamic vapour sorption (DVS) measurements with Raman spectroscopy, this innovative approach provides a more detailed and accurate measurement of the sorption isotherms than common methods. Moreover, we developed an approach for precisely predicting the sorption equilibria in three-component systems just based on sorption data of the corresponding binary subsystems. Our modelling approach combines the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) with the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP). Building on the description of the sorption isotherms of either water or ethanol in poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64) and in indomethacin (IND), we were able to quantitatively predict the simultaneous sorption of water and ethanol in PVPVA64 and the one of ethanol in an IND/PVPVA64 ASD.

Study on the flow characteristics of double-cone in hypersonic flows

Reusable spacecraft is one of the hot topics in the field of aerospace, attracting wide attention from researchers. Due to the high-Mach-number flight of re-entry, the air near the wall exhibits significant thermochemical nonequilibrium effects. Besides, the existing shock wave/boundary layer interaction (SWBLI) leads to severe aerodynamic heating issues. This study utilizes the two-temperature model to conduct simulations of hypersonic laminar flows around a canonical 25°/55° double-cone with low and high enthalpy. By varying the wall temperature and the aft cone angle, the evolution mechanism of the flow under the high-enthalpy and hypersonic freestream is explored. Our findings illustrate that while the thermodynamic nonequilibrium model closely reflects the separation zone evidenced in the experiments, it habitually overpredicts the peak heat transfer, particularly under high-enthalpy conditions. For the thermochemical nonequilibrium model, the flow field structure appears more uniform, with a reduced standoff distance of the detached shock. An incremental rise in wall temperature correlates with a proportional augmentation of the separation bubble, though its impact on the overall flow field is negligible. Increasing the aft cone angle intensifies the shock/shock interaction (SSI), transitioning from a lower-intensity Type VI to a more intense Type IV shock interplay. The examination reveals that the increase in temperature and cone angle amplifies the interaction between the separation region and shock waves, drastically escalating the peak heat transfer and fostering a secondary peak. The hypersonic flow of the double-cone demonstrates a multifaceted interaction of phenomena, notably SWBLI and SSI, with our analyses providing pivotal insights for the aerodynamic and thermal protection design of the high-Mach-number spacecraft.

Theoretical Analysis of Self-Shrinkage Spheroidization of Irregular Degradable Polymer Powder under Thermodynamic Nonequilibrium State

Laser three-dimensional (3D) printing offers significant advantages in integrating the shape and function of regenerative tissues through biomimetic manufacturing. However, its effectiveness is limited by the lack of specialized biopolymer powders—while solvent methods that use residual solvents produce powders with poor biocompatibility, mechanical methods result in irregularly shaped crystals. In this study, a biopolymer powder spheroidization and shaping technology, which utilizes the evolution of irregular powders into spheres with minimal surface free energy in the molten state, is proposed based on the thermodynamic principle of minimum energy. Initially, the motion trajectory and temperature field of the poly(L-lactic acid) (PLLA) powder during spheroidization were quantitatively assessed and optimized using Stokes’ law and Fourier's principle. Subsequently, the cohesive forces and aggregation kinetics of the polymer chains were calculated using molecular dynamics. Finally, based on these calculations, a phase-field model was constructed to simulate the evolution of the spheroidization rate and deduce the optimal parameters for the process. This precise approach enhances PLLA spheroidization control for laser 3D printing, improves part densification and surface quality, and offers a clean and efficient path for preparing high-quality PLLA spheroidized powder for laser 3D printing.

Development of a model of the process of development of manufacturing defects in automation means

In automated process control systems, automation equipment (sensors, converters, amplifiers, etc.) with technical defects arising during their manufacture, which are one of the main causes of failures, is widely used. The paper establishes the possibility of using the laws of nonequilibrium thermodynamics as the basis for determining the relationship between the controlled parameters of automation equipment and the parameters of the displayed medium, which made it possible to build a deterministic model of the development of production defects and, ultimately, determine the directions for changing and adjusting the technological processes of production of automation equipment. A method has been developed for implementing a guaranteed forecast of changes in the parameters of automation equipment based on solving the evolution equation using optimal filtering algorithms, which is the subject of research. The purpose of the work is to improve the quality and reliability of automation equipment by improving the monitoring of defects arising in the production of instruments, functional units and sensors of automation equipment. The article solves the following problems: analysis of existing approaches to the problem of manufacturing defects and methods for their detection and setting a research task; modeling of the process of development of production defects causing changes in the technical condition of automation equipment; development of a decision-making method based on guaranteed prediction of the technical state of automation equipment. The methodology of work is based on the methods of thermodynamic description of the kinetics of processes (when developing a model of the process of development of production defects that cause a change in technical condition) and methods of assessment and forecasting based on optimal filtering algorithms (when developing a decision-making method based on guaranteed foresight of technical condition). The results of the work include a model of the process of development of manufacturing defects that cause a change in the technical condition of automation equipment, and a decision-making method based on a guaranteed forecast of the technical condition of automation equipment. Conclusions. The paper establishes the possibility of using the laws of nonequilibrium thermodynamics to determine the relationship between the controlled parameters of automation equipment and the displayed medium, and to build a deterministic thermodynamic model of the development of production defects. Disclosed is an equation of evolution of technical state of automation equipment based on a deterministic kinetic model of processes occurring in a multicomponent medium, and an observation model which takes into account errors caused by instability of external effects and measurement errors. Disclosed is a method of implementing a guaranteed forecast of change in parameters of automation equipment based on solving the evolution equation using optimal filtering algorithms, which are used to solve estimation and prediction problems.

On the Elimination of Fast Variables from the Langevin Equation.

In a multivariable system, there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux-force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables in such a way that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof that Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.

Subaru/CHARIS High-resolution Mode Spectroscopy of the Brown Dwarf Companion HD 33632 Ab

Brown dwarfs (BDs) are model degenerate in age and mass. High-contrast imaging and spectroscopy of BD companions to host stars where the mass and age can be independently constrained by dynamics and stellar age indicators, respectively, provide valuable tests of BD evolution models. In this paper, we present a new epoch of Subaru/CHARIS H- and K-band observations of one such previously discovered system, HD 33632 Ab. We reanalyze the mass and orbit using our new epoch of extracted relative astrometry and fit extracted spectra to the newest generation of equilibrium, disequilibrium, and cloudy spectral and evolution models for BDs. No spectral model perfectly agrees with evolutionary tracks and the derived mass and age, instead favoring a somewhat younger BD than the host star’s inferred age. This tension can potentially be resolved using atmosphere and evolution models that consider both clouds and disequilibrium chemistry simultaneously or by additional future spectra at higher resolution or in other band passes. Photometric measurements alone remain consistent with the luminosity predicted by evolutionary tracks. Our work highlights the importance of considering complexities like clouds, disequilibrium chemistry, and composition when comparing spectral models to evolutionary tracks.

Thermodynamics and dynamic stability: extended theories of heat conduction

Abstract The stability of homogeneous thermodynamic equilibrium is analyzed in heat conduction theories in the framework of nonequilibrium thermodynamics, where the internal energy, the heat flux and a second order tensor are thermodynamic state variables. It is shown, that the thermodynamic conditions of concave entropy and nonnegative entropy production can ensure the linear stability. Various special heat conduction theories, including Extended Thermodynamics, are compared in the general framework.

Thermodynamic quantum Fokker–Planck equations and their application to thermostatic Stirling engine

We developed a computer code for the thermodynamic quantum Fokker–Planck equations (T-QFPE), derived from a thermodynamic system–bath model. This model consists of an anharmonic subsystem coupled to multiple Ohmic baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code numerically integrates the T-QFPE and their classical expression to simulate isothermal, isentropic, thermostatic, and entropic processes in both quantum and classical cases. The accuracy of the results was verified by comparing the analytical solutions of the Brownian oscillator. In addition, we illustrated a breakdown of the Markovian Lindblad-master equation in the pure quantum regime. As a demonstration, we simulated a thermostatic Stirling engine employed to develop non-equilibrium thermodynamics [S. Koyanagi and Y. Tanimura, J. Chem. Phys. 161, 114113 (2024)] under quasi-static conditions. The quasi-static thermodynamic potentials, described as intensive and extensive variables, were depicted as work diagrams. In the classical case, the work done by the external field is independent of the system–bath coupling strength. In contrast, in the quantum case, the work decreases as the coupling strength increases due to quantum entanglement between the subsystem and bath. The codes were developed for multicore processors using Open Multi-Processing (OpenMP) and for graphics processing units using the Compute Unified Device Architecture. These codes are provided in the supplementary material.

From de Sitter to de Sitter: A Thermal Approach to Running Vacuum Cosmology and the Non-Canonical Scalar Field Description

The entire classical cosmological history between two extreme de Sitter vacuum solutions is discussed based on Einstein’s equations and non-equilibrium thermodynamics. The initial non-singular de Sitter state is characterised by a very high energy scale, which is equal or smaller than the reduced Planck mass. It is structurally unstable, and all of the continuous created matter, energy, and entropy of the material component comes from the irreversible flow powered by the primeval vacuum energy density. The analytical expression describing the running vacuum is obtained from the thermal approach. It opens a new perspective to solve the old puzzles and current observational challenges plaguing the cosmic concordance model driven by a rigid vacuum. Such a scenario is also modelled through a non-canonical scalar field. It is demonstrated that the resulting scalar field model is shown to be a step-by-step a faithful analytical representation of the thermal running vacuum cosmology.