How Flexible Is the Concept of Local Thermodynamic Equilibrium?

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Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs–Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosion is identified as a thermodynamically stable motion. In the second approach, we use a thermodynamic Lyapunov function and its time rate from the Lyapunov thermodynamic stability theory (LTS, previously known as CTTSIP). In doing so, we demonstrate that the second differential of entropy, a frequently used Lyapunov function, is useful only for investigating the stability of equilibrium states. Nonequilibrium steady states do not qualify. Without using explicit perturbation coordinates, we further identify asymptotic thermodynamic stability and thermodynamic stability under constantly acting disturbances of unperturbed trajectories as well as of nonequilibrium steady states. The third approach is also based on the Lyapunov function from LTS, but here we additionally use the rates of perturbation coordinates, based on the Gibbs relations and without using their explicit expressions, to identify not only asymptotic thermodynamic stability but also thermodynamic stability under constantly acting disturbances. Only those trajectories leading to an infinite rate of entropy production (unstable states) are excluded from this conclusion. Finally, we use these findings to formulate the Fourth Law of thermodynamics based on the thermodynamic stability. It is a comprehensive statement covering all nonequilibrium trajectories, close to as well as far from equilibrium. Unlike previous suggested “fourth laws”, this one meets the same level of generality that is associated with the original zeroth to third laws. The above is illustrated using the Schlögl reaction with its multiple steady states in certain regions of operation.

and at the local level

where

is the exchange-of-entropy differential,

is the entropy production differential,

is the mass density, s is the per unit mass entropy,

is the entropy flux density, and

is the entropy source strength. A simpler version of Equation ( 7 ) is …”

Section: Gibbs–duhem Theory Of Stability Of Irreversible Processesmentioning

confidence: 99%

“…For the sake of demonstration, we used the Gibbs relation of phenomenological irreversible thermodynamics, PIT (previously named GPITT) (see, for example, the recent publication [ 68 ]). The local-level Gibbs relation of PIT for a spatially nonuniform system is

…”

Section: Using Thermodynamic Variables Based On Gibbs Relations and T...mentioning

confidence: 99%

Thermodynamic Stability Theories of Irreversible Processes and the Fourth Law of Thermodynamics

Tangde,

Bhalekar,

Andresen

2024

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“…CIT theory in the non-linear regime establishes the existence of multiple, locally stable, dissipative stationary states, consisting of processes (flows) which can break space and time symmetry (dissipative structuring), for a system interacting with its environment. CIT theory has been empirically validated for situations in which a macroscopic local thermodynamic equilibrium in space and time can be established, a restriction observed for most terrestrial, sufficiently dense, material systems [14], including "fast" systems involving, for example, photon-induced quantum electronic excitations [31].…”

Section: Origin Of the Second Law And Irreversible Thermodynamic Theorymentioning

confidence: 99%

The Non-Equilibrium Thermodynamics of Natural Selection: From Molecules to the Biosphere

Michaelian

2023

Evolutionary theory suggests that the origin, persistence, and evolution of biology is driven by the “natural selection” of characteristics improving the differential reproductive success of the organism in the given environment. The theory, however, lacks physical foundation, and, therefore, at best, can only be considered a heuristic narrative, of some utility for assimilating the biological and paleontological data at the level of the organism. On deeper analysis, it becomes apparent that this narrative is plagued with problems and paradoxes. Alternatively, non-equilibrium thermodynamic theory, derived from physical law, provides a physical foundation for describing material interaction with its environment at all scales. Here we describe a “natural thermodynamic selection” of characteristics of structures (or processes), based stochastically on increases in the global rate of dissipation of the prevailing solar spectrum. Different mechanisms of thermodynamic selection are delineated for the different biotic-abiotic levels, from the molecular level at the origin of life, up to the level of the present biosphere with non-linear coupling of biotic and abiotic processes. At the levels of the organism and the biosphere, the non-equilibrium thermodynamic description of evolution resembles, respectively, the Darwinian and Gaia descriptions, although the underlying mechanisms and the objective function of selection are fundamentally very different.

“…where τ denotes a relaxation time and a is a material parameter. Despite the use of numerous alternative models and extensive research, the question of a suitable non-Fourier heat conduction model still remains open [32,33].…”

Section: Heat Conduction In Rigid Solidsmentioning

confidence: 99%

“…together with pressure relation (33), transforms dissipation inequality (88) into the linear combination of products of thermodynamic fluxes and forces:…”

Section: Viscous Fluidsmentioning

confidence: 99%

Constitutive Modeling with Single and Dual Internal Variables

Berezovski

2023

Phenomenological constitutive models with internal variables have been applied for a wide range of material behavior. The developed models can be classified as related to the single internal variable formalism based on the thermodynamic approach by Coleman and Gurtin. The extension of this theory to so-called dual internal variables opens up new avenues for the constitutive modeling of macroscopic material behavior. This paper reveals the distinction between constitutive modeling with single and dual internal variables using examples of heat conduction in rigid solids, linear thermoelasticity, and viscous fluids. A thermodynamically consistent framework for treating internal variables with as little a priori knowledge as possible is presented. This framework is based on the exploitation of the Clausius–Duhem inequality. Since the considered internal variables are “observable but not controllable”, only the Onsagerian procedure with the use of the extra entropy flux is appropriate for the derivation of evolution equations for internal variables. The key distinctions between single and dual internal variables are that the evolution equations are parabolic in the case of a single internal variable and hyperbolic if dual internal variables are employed.