Classical Equilibrium Thermodynamics Research Articles

Anomalous, dielectrophoretic transport of molecules in non-electrolytes.

The electric field (E-field) dielectric polarization-based separations mechanism represents a novel method for separating solutions at small length scales. An E-field gradient with a maximum strength of 0.4 MV/m applied across a 10μm deep channel is shown to increase the concentration inside the low E-field region by ≈ 40% relative to the high E-field region. This concentration change is two orders of magnitude higher than the estimated change predicted using the classical equilibrium thermodynamics for the same E-field. The deviation between the predicted and the experimental results suggests that the change in volumetric E-field energy with solute concentration is insufficient to explain this phenomenon. The study also explores the effect of varying strength of E-field and frequency of supplied voltage on the dielectric polarization-based separation efficiency. While the increase in the former increases the separation efficiency, the increase in the latter reduces the degree of concentration change due to ineffective charging of the electrodes.

Success versus failure: Efficient heat devices in thermodynamics.

Classical equilibrium thermodynamics provides, in a general way, upper Carnot bounds for the performance of energy converters. Nevertheless, to suggest lower bounds is a much more subtle issue, especially when they are related to a definition of convenience. Here, this issue is investigated in a unified way for heat engines, refrigerators, and heat pumps. First, irreversibilities are weighted in the context of heat reservoir stability for irreversible engines by using the thermodynamic distance between minimum energy and maximum entropy steady states. Some stability coefficients can be related to a majorization process and the obtention of Pareto fronts, linking stability and optimization by means of efficiency and entropy due to correlations between system and reservoirs. Second, these findings are interpreted in a very simple context. A region where the heat device is efficient is defined in a general scheme and, below this zone, the heat device is inefficient in the sense that irreversibilities somehow dominate its behavior. These findings allow for a clearer understanding of the role played by some well-known figures of merit in the scope of finite-time and -size optimization. Comparison with experimental results is provided.

Understanding the thermodynamic properties of insect swarms

Sinhuber et al. (Sci Rep 11:3773, 2021) formulated an equation of state for laboratory swarms of the non-biting midge Chironomus riparius that holds true when the swarms are driven through thermodynamic cycles by the application external perturbations. The findings are significant because they demonstrate the surprising efficacy of classical equilibrium thermodynamics for quantitatively characterizing and predicting collective behaviour in biology. Nonetheless, the equation of state obtained by Sinhuber et al. (2021) is anomalous, lacking a physical analogue, making its’ interpretation problematic. Moreover, the dynamical processes underlying the thermodynamic cycling were not identified. Here I show that insect swarms are equally well represented as van der Waals gases and I attribute the possibility of thermodynamic cycling to insect swarms consisting of several overlapping sublayers. This brings about a profound change in the understanding of laboratory swarms which until now have been regarded as consisting of non-interacting individuals and lacking any internal structure. I show how the effective interactions can be attributed to the swarms’ internal structure, the external perturbations and to the presence of intrinsic noise. I thereby show that intrinsic noise which is known to be crucial for the emergence of the macroscopic mechanical properties of insect swarms is also crucial for the emergence of their thermodynamic properties as encapsulated by their equation of state.

Equilibrium thermodynamics and the genesis of protein\u2013protein complexes in cells

It is often thought that the structural complexity of living organisms places Life outside the laws of Physics. According to the Second Law of Thermodynamics, inanimate matter tends towards ever-increasing randomness. Most thermodynamic studies on the living system are course-grained in the sense that it is the whole organism which is considered and they lack microscopic details. In these studies, as the living system is an open system, non-linear thermodynamics have been used. This requires that a number of assumptions be made concerning the living system itself, which may not be correct in organisms living under natural environmental conditions. In the present study, we depart from this approach and use a fine-grained analysis of the genesis of subcellular protein complex structures. The analysis is performed in terms of classical equilibrium thermodynamics using the acquired knowledge of protein/protein interactions. In this way, it is demonstrated that the spontaneous creation of ordered subcellular structures occurs in accordance with the Second Law of Thermodynamics. We specifically consider the simple example of protein dimer and trimer formation from its monomer components, both in vitro and with chaperone assistance in vivo. The entropy decrease associated with protein complex assembly, on which the continuing debate is founded, is shown to be a relatively small component in the overall and positive entropy increase.Graphic abstract

Irreversible work and Maxwell demon in terms of quantum thermodynamic force

The second law of classical equilibrium thermodynamics, based on the positivity of entropy production, asserts that any process occurs only in a direction that some information may be lost (flow out of the system) due to the irreversibility inside the system. However, any thermodynamic system can exhibit fluctuations in which negative entropy production may be observed. In particular, in stochastic quantum processes due to quantum correlations and also memory effects we may see the reversal energy flow (heat flow from the cold system to the hot system) and the backflow of information into the system that leads to the negativity of the entropy production which is an apparent violation of the Second Law. In order to resolve this apparent violation, we will try to properly extend the Second Law to quantum processes by incorporating information explicitly into the Second Law. We will also provide a thermodynamic operational meaning for the flow and backflow of information. Finally, it is shown that negative and positive entropy production can be described by a quantum thermodynamic force.

Role of Gaussian curvature on local equilibrium and dynamics of smectic-isotropic interfaces

Recent research on interfacial instabilities of smectic films has shown unexpected morphologies that are not fully explained by classical local equilibrium thermodynamics. Annealing focal conic domains can lead to conical pyramids, changing the sign of the Gaussian curvature and exposing smectic layers at the interface. In order to explore the role of the Gaussian curvature on the stability and evolution of the film-vapor interface, we introduce a phase-field model of a smectic-isotropic system as a first step in the study. Through asymptotic analysis of the model, we generalize the classical condition of local equilibrium, the Gibbs-Thomson equation, to include contributions from surface bending and torsion and a dependence on the layer orientation at the interface. A full numerical solution of the phase-field model is then used to study the evolution of focal conic structures in smectic domains in contact with the isotropic phase via local evaporation and condensation of smectic layers. As in experiments, numerical solutions show that pyramidal structures emerge near the center of the focal conic owing to evaporation of adjacent smectic planes and to their orientation relative to the interface. Near the center of the focal conic domain, a correct description of the motion of the interface requires the additional curvature terms obtained in the asymptotic analysis, thus clarifying the limitations in modeling motion of hyperbolic surfaces solely driven by mean curvature.

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.

Development of propositions and models of classical equilibrium thermodynamics and their application in energy research

Development of propositions and models of classical equilibrium thermodynamics and their application in energy research

Critical memory capacity of Hopfield model implemented in coherent Ising machine

The coherent Ising machine (CIM) has attracted attention as one of the most effective Ising computing architectures for solving large-scale optimization problems because of its scalability and high-speed computational ability. The CIM is a non-equilibrium open-dissipative system, so the theories and techniques of classical equilibrium thermodynamics cannot be directly applied to it. Our research group has adapted these theories and techniques to work with the CIM. Here, we focus on an infinite loading Hopfield model, which is a canonical frustrated model of Ising computation. We derive a macroscopic equation to elucidate the relation between critical memory capacity and normalized pump rate in the CIM-implemented Hopfield model.

Conventional Hydraulic Circuits in an Analysis of Environmental Issues

The paper addresses the problems of conventional circuit modeling in an analysis of anthropogenic pollution of nature. A joint use of two types of models is proposed: 1) a model of conventional hydraulic circuits and 2) a model of extreme intermediate states developed by Melentiev Energy Systems Institute. The first model is used to calculate the distribution of pollutants in the atmosphere and their precipitation. The second model is intended for an analysis of the formation of pollutants and their transformations in branches as a result of chemical reactions and phase transitions. The analysis is based on the propositions of classical equilibrium thermodynamics. The applicability of the thermodynamic equilibrium and extremality principles and one-dimensional circuit models in the study of both reversible and irreversible processes are substantiated. Specific problems are analyzed. These are the determination of the yield of harmful substances in fuel combustion and processing, the distribution of pollutants in the atmosphere of large regions, the impact of hydro and wind power plants on the formation of harmful solutions in the air. The possibility of using a conventional graph (a thermodynamic tree) proposed by A.N. Gorban to analyze fuel technologies is demonstrated. The statement of the problem related to the assessment of the environmental compatibility of integrated energy systems is presented. The admissibility of the representation of the optimal distribution of flows in the integrated system as a sum of optimal distributions in its subsystems that differ from one another in physical-technical and economic nature is explained.

The role of Minkowski functionals in the thermodynamics of two-phase systems

Within this work quite old concepts from integral geometry are applied to classical equilibrium thermodynamics of two-phase systems. In addition to the area as basic interfacial quantity the full geometric characterization of the interface is used, which includes the two remaining Minkowski functionals, the mean curvature integral and the Euler Poincaré characteristic. The basic energetic characteristic of the interface (i.e. the interfacial tension) is extended by two additional properties: edge force as (up to a factor 4/π) the work necessary to form a right-angled edge of unit length, and item energy as the work to form an additional item in the phase morphology. Both quantities are of increasing importance, when going to micro- and nano-scales. They are subsequently used for interfaces of arbitrary shape to derive a relationship extending the classical Young-Laplace equation. The supplementary contribution is proportional to the Gaussian curvature, with the edge force as proportionality constant. Furthermore, both edge force and item energy are shown to be applicable to the description of crystal nucleation in liquids (extending the classical Becker Döring theory). It turns out, that even above the thermodynamic melting temperature stable nuclei can be present in the liquid phase. They immediately are able to grow when quenched to a temperature below a characteristic temperature. This temperature of spontaneous homogeneous nucleation is simply connected to the edge force, whereas the number of stable clusters per unit volume is dominated by the item energy. Finally, the additional energetic interfacial properties are used in a similar way to characterize the stability of emulsions.

Coherent Application of a Contact Structure to Formulate Classical Non-Equilibrium Thermodynamics

This contribution presents an outline of a new mathematical formulation for Classical Non-Equilibrium Thermodynamics (CNET) based on a contact structure in differential geometry. First a non-equilibrium state space is introduced as the third key element besides the first and second law of thermodynamics. This state space provides the mathematical structure to generalize the Gibbs fundamental relation to non-equilibrium thermodynamics. A unique formulation for the second law of thermodynamics is postulated and it showed how the complying concept for non-equilibrium entropy is retrieved. The foundation of this formulation is a physical quantity, which is in non-equilibrium thermodynamics nowhere equal to zero. This is another perspective compared to the inequality, which is used in most other formulations in the literature. Based on this mathematical framework, it is proven that the thermodynamic potential is defined by the Gibbs free energy. The set of conjugated coordinates in the mathematical structure for the Gibbs fundamental relation will be identified for single component, closed systems. Only in the final section of this contribution will the equilibrium constraint be introduced and applied to obtain some familiar formulations for classical (equilibrium) thermodynamics.

Thermodynamic analysis of environmental problems of energy

The paper discusses the problems of the ecological analysis of physicochemical processes in power units and the impact of energy systems on the nature in large territorial regions. The model of extreme intermediate states developed at the Energy Systems Institute based on the principles of classical equilibrium thermodynamics was chosen to devise specific computational methods. The results of the conducted studies are presented and directions for further work are outlined.

Non-Boltzmann stationary distributions and nonequilibrium relations in active baths.

Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and therefore cannot be treated within the framework of classical equilibrium thermodynamics. Here we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the nonequilibrium fluctuations associated with an active bath. We show in particular that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, nonequilibrium relations (e.g., the Jarzynski equality and Crooks fluctuation theorem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments.

Thermodynamic restrictions on linear reversible and irreversible thermo-electro-magneto-mechanical processes.

A unified thermodynamic framework for the characterization of functional materials is developed. This framework encompasses linear reversible and irreversible processes with thermal, electrical, magnetic, and/or mechanical effects coupled. The comprehensive framework combines the principles of classical equilibrium and non-equilibrium thermodynamics with electrodynamics of continua in the infinitesimal strain regime.In the first part of this paper, linear Thermo-Electro-Magneto-Mechanical (TEMM) quasistatic processes are characterized. Thermodynamic stability conditions are further imposed on the linear constitutive model and restrictions on the corresponding material constants are derived. The framework is then extended to irreversible transport phenomena including thermoelectric, thermomagnetic and the state-of-the-art spintronic and spin caloritronic effects. Using Onsager's reciprocity relationships and the dissipation inequality, restrictions on the kinetic coefficients corresponding to charge, heat and spin transport processes are derived. All the constitutive models are accompanied by multiphysics interaction diagrams that highlight the various processes that can be characterized using this framework.

Open system trajectories specify fluctuating work but not heat.

Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated. Yet, even though the Hamiltonian of mean force uniquely determines the equilibrium phase space probability density of a strongly coupled open system, the knowledge of this probability density alone is insufficient to determine the Hamiltonian of mean force, needed in constructing the underlying statistical mechanics and thermodynamics. We demonstrate that under the assumption that the Hamiltonian of mean force is known, an extension of thermodynamic structures from the level of averaged quantities to fluctuating objects (i.e., a stochastic thermodynamics) is possible. However, such a construction undesirably also involves a vast ambiguity. This situation is rooted in the eminent lack of a physical guiding principle allowing us to distinguish a physically meaningful theory out of a multitude of other equally conceivable ones.

A Derivation of the Gibbs Equation and the Determination of Change in Gibbs Entropy from Calorimetry

In this paper, we give a succinct derivation of the fundamental equation of classical equilibrium thermodynamics, namely the Gibbs equation. This derivation builds on our equilibrium relaxation theorem for systems in contact with a heat reservoir. We reinforce the comments made over a century ago, pointing out that Clausius’ strict inequality for a system of interest is within Clausius’ set of definitions, logically undefined. Using a specific definition of temperature that we have recently introduced and which is valid for both reversible and irreversible processes, we can define a property that we call the change in calorimetric entropy for these processes. We then demonstrate the instantaneous equivalence of the change in calorimetric entropy, which is defined using heat transfer and our definition of temperature, and the change in Gibbs entropy, which is defined in terms of the full N-particle phase space distribution function. The result shows that the change in Gibbs entropy can be expressed in terms of physical quantities.

Mathematical models and numerical methods for the simulation of adaptive inflatable structures for impact absorption

The paper describes various approaches for the mathematical modelling of Adaptive Inflatable Structures (AIS) along with the corresponding numerical methods. The introductory part presents a general idea of adaptive impact absorption (AIA) and the concept of inflatable structures equipped with controllable valves serving for internal pressure control. Application of AIS for adaptive absorption of the impact loading is briefly explained. The paper focuses on diverse methods of modelling of inflatable structures, which are based on interaction between solid walls and fluid enclosed inside. Modelling of the solid walls is based on rigid body dynamics or initial-boundary value problem of solid mechanics. In turn, modelling of the fluid utilizes either classical equilibrium thermodynamics or Navier–Stokes equations. Consequently, four possible combinations of the above approaches are distinguished, precisely analyzed and applied for the modelling of different types of inflatable structures. Each model takes into account controllable valves, which requires introducing additional coupling between parameters defining the valves and selected results of the analysis. Corresponding numerical methods include classical methods of solving ordinary differential equations, finite volume method (FVM) applied for problems with mobile boundaries, finite element method (FEM) applied for problems involving additional ODEs and, finally, FEM coupled with FVM. Proposed numerical methods and software tools are utilized for the simulation of adaptive pneumatic cylinders, adaptive pneumatic fenders and membrane valves.

Contact Geometry of Mesoscopic Thermodynamics and Dynamics

The time evolution during which macroscopic systems reach thermodynamic equilibrium states proceeds as a continuous sequence of contact structure preserving transformations maximizing the entropy. This viewpoint of mesoscopic thermodynamics and dynamics provides a unified setting for the classical equilibrium and nonequilibrium thermodynamics, kinetic theory, and statistical mechanics. One of the illustrations presented in the paper is a new version of extended nonequilibrium thermodynamics with fluxes as extra state variables.

Thermodynamic modeling of fully coupled finite-deformation thermo-electro-magneto-mechanical behavior for multifunctional applications

In this paper, we model fully coupled thermo-electro-magneto-mechanical (TEMM) behavior in the finite-deformation regime by (i) developing for the first time a comprehensive catalogue of free energies, state variables, and state equations, and (ii) combining this catalogue with the first principles of nonlinear continuum electrodynamics. We develop our catalogue in a thermodynamically consistent manner, and circumvent the ambiguities and challenges inherent in nonlinear continuum electrodynamics, by connecting with classical equilibrium thermodynamics. We use its formalism as a blueprint for characterizing a fundamental energetic process, that is, one where internal energy is the characterizing potential, the independent variables are extensive, and the dependent variables are intensive. A key feature of identifying this fundamental energetic process is the resulting ability to transparently and rigorously introduce new free energies – many appearing in the finite-deformation TEMM literature for the first time – that employ any set of intensive or extensive quantities as independent variables. We also develop novel mathematical transformations that accommodate alternative electromagnetic work conjugates as independent variables.Each thermodynamic potential in our comprehensive catalogue characterizes a particular thermo-electro-magneto-mechanical process. Each process, in turn, correlates with a particular experiment, the independent variables being controlled and the dependent variables being the measured responses. Our framework will thus enable the development of constitutive models for multifunctional materials under different experimental conditions. Additionally, the research presented herein can be used to convert targeted performance properties that are inherently nonlinear, three dimensional, and anisotropic into a “recipe” for multifunctional material design.