CLASSICAL AND MULTISCALE NON-EQUILIBRIUM THERMODYNAMICS

A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It is shown here that such a modification not only makes it possible to deductively obtain the main results of classical linear nonequilibrium thermodynamics, but also provides evidence for a number of statements for a nonlinear case (the maximum entropy production principle, the macroscopic reversibility principle, and generalized reciprocity relations) that are under discussion in the literature.

Thermal cycles in classical thermodynamics and nonequilibrium thermodynamics in contrast with finite time thermodynamics

This contribution presents an outline of a new mathematical formulation for<br/>Classical Non-Equilibrium Thermodynamics (CNET) based on a contact<br/>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.<br/>This state space provides the mathematical structure to generalize<br/>the Gibbs fundamental relation to non-equilibrium thermodynamics. A<br/>unique formulation for the second law of thermodynamics is postulated and it<br/>showed how the complying concept for non-equilibrium entropy is retrieved.<br/>The foundation of this formulation is a physical quantity, which is in nonequilibrium 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<br/>thermodynamic potential is defined by the Gibbs free energy. The set of conjugated coordinates in the mathematical structure for the Gibbs fundamental<br/>relation will be identified for single component, closed systems. Only in the<br/>final section of this contribution will the equilibrium constraint be introduced<br/>and applied to obtain some familiar formulations for classical (equilibrium)<br/>thermodynamics.

Recent measurements of the temperature profile across the interface of an evaporating liquid are in strong disagreement with the predictions from classical kinetic theory or nonequilibrium thermodynamics. However, these previous measurements in the vapor were made within a minimum of 27 mean free paths of the interface. Since classical kinetic theory indicates that sharp changes in the temperature can occur near the interface of an evaporating liquid, a series of experiments were performed to determine if the disagreement could be resolved by measurements of the temperature closer to the interface. The measurements reported herein were performed as close as one mean free path of the interface of an evaporating liquid. The results indicate that it is the higher-energy molecules that escape the liquid during evaporation. Their temperature is greater than that in the liquid phase at the interface and as a result there is a discontinuity in temperature across the interface that is much larger in magnitude (up to 7.8 \ifmmode^\circ\else\textdegree\fi{}C in our experiments) and in the opposite direction to that predicted by classical kinetic theory or nonequilibrium thermodynamics. The measurements reported herein support the previous ones.

Starting from the second law of thermodynamics applied to an isolated system consisting of the system surrounded by an extremely large medium, we formulate a general nonequilibrium thermodynamic description of the system when it is out of thermal and mechanical equilibrium with the medium. Our approach allows us to identify the correct form of the Gibbs free energy and enthalpy. We also obtain an extension of the classical nonequilibrium thermodynamics due to de Donder in which one normally assumes thermal and mechanical equilibrium with the medium; see text. We find that the temperature and pressure differences between the system and the medium act as thermodynamic forces, which are normally neglected in the classical nonequilibrium thermodynamics. The Prigogine-Defay ratio is found to be greater than 1 merely due to the lack of equilibrium with the medium, even though we do not consider any internal order parameters. This shows that these forces should play an important role in relaxation processes. We then apply our approach to study the general trend during structural relaxation in glasses and establish the phenomenology behind the concept of the fictive temperature and of the empirical Tool-Narayanaswamy equation on firmer theoretical foundation.

Chapter 4 - Thermodynamics of nanoparticle–cell interaction

Chapter 12 - The Nonequilibrium Thermodynamics of Radiation Interaction

This book is a collection of chapters which report on recent developments in the field of non-equilibrium thermodynamics. It is meant for readers that would like to know what the field can add to their understanding of transport phenomena, or what it means for experimental design. Classical non-equilibrium thermodynamics was established in 1931 and developed during the subsequent thirty years for transport in homogeneous phases. This chapter gives a short presentation of the basic assumptions, along with advice on how to derive the entropy production and find the flux–force relations for transport of heat, mass and charge. In the end of the chapter, we put the subsequent chapters of the book into perspective. The book presents recent results for homogeneous systems, for mesoscopic systems and for heterogeneous systems.

The entropy production is expressed as the product of the generalized force (driving force) and generalized flux, which plays a central role in classical non-equilibrium thermodynamics. This expression has shortcomings in two aspects: first, the decomposition into generalized fluxes and forces is arbitrary to some extent; more importantly, the entropy production is negative value calculated in heat wave propagation, which breaks the second law. In this paper, we carry out analyses based on the thermomass theory and show that the entropy production is induced by the dissipation of thermomass energy during heat condution. The generalized force of entropy production is not driving force but resistive force, having a unit of force in Newton’s mechanics. The modified expression for entropy production not only guarantees its positiveness in propagation of heat waves consistent with the extended irreversible thermodynamics, but also avoids the arbitrariness of decomposition.

In order to extend the range of application of classical irreversible thermodynamics far from equilibrium, an extension of the Gibbs equation is presented. The new Gibbs equation is assumed to contain, besides its usual contributions, supplementary terms equal to the thermodynamic fluxes. The entropy flux and the entropy production also take more general forms than in classical non-equilibrium thermodynamics. As an illustration of the formalism, an isotropic viscous and non-isothermal two-fluid mixture is considered. The results are shown to be in agreement with the Boltzmann kinetic theory.

Thermal energy storage processes involve the storage of energy in one or more forms of internal, kinetic, potential and chemical; transformation between these energy forms; and transfer of energy. Thermodynamics is a science that deals with storage, transformation and transfer of energy and is therefore fundamental to thermal energy storage. Thermodynamics can be categorised into classical thermodynamics, statistical mechanics, chemical thermodynamics, equilibrium thermodynamics and non-equilibrium thermodynamics. This chapter introduces classical thermodynamics concepts and laws although they are applicable to other categories. An attempt is made to relate these to thermal energy storage where appropriate.

Equations describing local thermal and caloric equations of state in heterogeneous systems at any degree of their states’ deviation from equilibrium are derived. The state of a system is described by equations of the transfer of mixture components; these generalize the equations of classical non-equilibrium thermodynamics for strongly nonequilibrium processes. The contributions from reactions and external fields are taken into account. The equations are derived using the lattice gas model with discrete molecular distributions in space (on a scale comparable to molecular dimensions) and continuous molecular distributions (at short distances inside cells) during their translational and vibrational motions. For simplicity, it is assumed that distinctions between the sizes of mixture components are small. Contributions from potential functions of intermolecular interaction (of the Lennard-Jones type) to some coordination spheres are considered. The theory provides a unified description of the dynamics of distributions of concentrations and pair functions of mixture components in three aggregate states, and at their interfaces. Universal expressions for the local components of the pressure tensor and internal energy inside multicomponent bulk phases and at their interfaces are obtained. Local components of the pressure tensor and the internal energy are universally expressed through local unary and pair distribution functions (DFs) in any nonequilibrium state. The time evolution of the unary and pair DFs themselves is determined from the derived system of equations of mass, momentum, and energy transfer that ensure the transition of the system from a strongly nonequilibrium state to both the local equilibrium state described within traditional nonequilibrium thermodynamics and the complete thermodynamic equilibrium state postulated by classical thermodynamics.

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.

This paper considers the modern approach to the thermodynamic modeling of developed turbulent flows of a compressible fluid based on the systematic application of the formalism of extended irreversible thermodynamics (EIT) that goes beyond the local equilibrium hypothesis, which is an inseparable attribute of classical nonequilibrium thermodynamics (CNT). In addition to the classical thermodynamic variables, EIT introduces new state parameters—dissipative flows and the means to obtain the respective evolutionary equations consistent with the second law of thermodynamics. The paper presents a detailed discussion of a number of physical and mathematical postulates and assumptions used to build a thermodynamic model of turbulence. A turbulized liquid is treated as an indiscrete continuum consisting of two thermodynamic sub-systems: an averaged motion subsystem and a turbulent chaos subsystem, where turbulent chaos is understood as a conglomerate of small-scale vortex bodies. Under the above formalism, this representation enables the construction of new models of continual mechanics to derive cause-and-effect differential equations for turbulent heat and impulse transfer, which describe, together with the averaged conservations laws, turbulent flows with transverse shear. Unlike gradient (noncausal) relationships for turbulent flows, these differential equations can be used to investigate both hereditary phenomena, i.e., phenomena with history or memory, and nonlocal and nonlinear effects. Thus, within EIT, the second-order turbulence models underlying the so-called invariant modeling of developed turbulence get a thermodynamic explanation. Since shear turbulent flows are widespread in nature, one can expect the given modification of the earlier developed thermodynamic approach to developed turbulence modeling (see Kolesnichenko, 1980; 1998; 2002–2004; Kolesnichenko and Marov, 1985; Kolesnichenko and Marov, 2009) to be used in research on a broad class of dissipative phenomena in various astro- and geophysical applications. In particular, a major application of the proposed approach is the reconstruction of the processes in the preplanetary circumsolar disk, which might help solve the fundamental problems of stellar-planetary cosmogony.

Analytical thermodynamics: by S. L. Soo. 437 pages, diagrams, 6 x 9 in. Englewood Cliffs, Prentice Hall, Inc., 1962. Price: $14.00 (trade); $10.50 (text)