scholarly journals Nonlinear Non-Equilibrium Thermodynamics Based on the Ehrenfest–Klein Model

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 293
Author(s):  
Gleb A. Zhernokleev ◽  
Leonid M. Martyushev
Keyword(s):  
Entropy Production ◽  
Fluctuation Theorem ◽  
Equilibrium Thermodynamic ◽  
Equilibrium Thermodynamics ◽  
Thermodynamic Entropy ◽  
Klein Model ◽  
Non Equilibrium

Nonlinear non-equilibrium thermodynamic relations have been constructed based on the generalized Ehrenfest–Klein model. Using these relations, the behavior of the entropy and its production in time at arbitrary deviations from equilibrium has been studied. It has been shown that the transient fluctuation theorem is valid for this model if a dissipation functional is treated as the thermodynamic entropy production.

Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution

2010 ◽  
Vol 368 (1910) ◽  
pp. 181-196 ◽  
Author(s):  
Axel Kleidon
Keyword(s):  
Entropy Production ◽  
Maximum Entropy ◽  
Thermodynamic Equilibrium ◽  
Earth System ◽  
Equilibrium Thermodynamic ◽  
Equilibrium Thermodynamics ◽  
System Evolution ◽  
The Earth ◽  
System Functioning ◽  
Non Equilibrium

The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system’s state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth’s past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning.

Local Entropy Production Rates in a Polymer Electrolyte Membrane Fuel Cell

2017 ◽  
Vol 42 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Marc Siemer ◽  
Tobias Marquardt ◽  
Gerardo Valadez Huerta ◽  
Stephan Kabelac
Keyword(s):  
Fuel Cell ◽  
Entropy Production ◽  
Polymer Electrolyte ◽  
Polymer Electrolyte Membrane ◽  
Gas Diffusion ◽  
Transport Processes ◽  
Local Entropy ◽  
Equilibrium Thermodynamics ◽  
Electrolyte Membrane ◽  
Non Equilibrium

AbstractA modeling study on a polymer electrolyte membrane fuel cell by means of non-equilibrium thermodynamics is presented. The developed model considers a one-dimensional cell in steady-state operation. The temperature, concentration and electric potential profiles are calculated for every domain of the cell. While the gas diffusion and the catalyst layers are calculated with established classical modeling approaches, the transport processes in the membrane are calculated with the phenomenological equations as dictated by the non-equilibrium thermodynamics. This approach is especially instructive for the membrane as the coupled transport mechanisms are dominant. The needed phenomenological coefficients are approximated on the base of conventional transport coefficients. Knowing the fluxes and their intrinsic corresponding forces, the local entropy production rate is calculated. Accordingly, the different loss mechanisms can be detected and quantified, which is important for cell and stack optimization.

A new perspective on the electron transfer: recovering the Butler–Volmer equation in non-equilibrium thermodynamics

2016 ◽  
Vol 18 (36) ◽  
pp. 24966-24983 ◽  
Author(s):  
Wolfgang Dreyer ◽  
Clemens Guhlke ◽  
Rüdiger Müller
Keyword(s):  
Electron Transfer ◽  
Asymptotic Analysis ◽  
Thermodynamic Model ◽  
Equilibrium Thermodynamic ◽  
Equilibrium Thermodynamics ◽  
Electrochemical Systems ◽  
New Perspective ◽  
Physical Phenomena ◽  
Insight Into ◽  
Non Equilibrium

Butler–Volmer equations can be recovered from a complete non-equilibrium thermodynamic model by application of asymptotic analysis. Thereby we gain insight into the coupling of different physical phenomena and can derive Butler–Volmer equations for very different materials and electrochemical systems.

NON-EQUILIBRIUM THERMODYNAMICS AND STOCHASTICS OF GOMPERTZIAN GROWTH

1996 ◽  
Vol 04 (02) ◽  
pp. 151-157 ◽  
Author(s):  
C.G. CHAKRABARTI ◽  
SYAMALI BHADRA
Keyword(s):  
Stochastic Model ◽  
Thermodynamic Modelling ◽  
Random Disturbance ◽  
Equilibrium Thermodynamic ◽  
Equilibrium Thermodynamics ◽  
Gompertzian Growth ◽  
Non Equilibrium

The paper deals with the non-equilibrium thermodynamic modelling of Gompertzian growth of a population substantiated by a stochastic model of the system under random disturbance of the environment.

Non-equilibrium thermodynamic potential and flux fluctuation theorem

2009 ◽  
Vol 373 (37) ◽  
pp. 3301-3303 ◽  
Author(s):  
M. Criado-Sancho ◽  
J. Casas-Vázquez ◽  
D. Jou
Keyword(s):  
Thermodynamic Potential ◽  
Fluctuation Theorem ◽  
Equilibrium Thermodynamic ◽  
Non Equilibrium

scholarly journals Dissipated work, stability and the internal flow structure of granular snow avalanches

2005 ◽  
Vol 51 (172) ◽  
pp. 125-138 ◽  
Author(s):  
Perry Bartelt ◽  
Othmar Buser ◽  
Martin Kern
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Dissipative Systems ◽  
Momentum Balance ◽  
Granular System ◽  
Snow Avalanches ◽  
Equilibrium Thermodynamics ◽  
Layer System ◽  
Constitutive Parameters ◽  
Non Equilibrium

AbstractWe derive work dissipation functionals for granular snow avalanches flowing in simple shear. Our intent is to apply constructive theorems of non-equilibrium thermodynamics to the snow avalanche problem. Snow chute experiments show that a bi-layer system consisting of a non-yielded flow plug overriding a sheared fluidized layer can be used to model avalanche flow. We show that for this type of constitutive behaviour the dissipation functionals are minimum at steady state with respect to variations in internal velocity; however, the functionals must be constrained by subsidiary mass- continuity integrals before the equivalence of momentum balance and minimal work dissipation can be established. Constitutive models that do not satisfy this equivalence are henceforth excluded from our consideration. Fluctuations in plug and slip velocity depend on the roughness of the flow surface and viscosity of the granular system. We speculate that this property explains the transition from flowing avalanches to powder avalanches. Because the temperature can safely be assumed constant, we demonstrate within the context of non-equilibrium thermodynamics that granular snow avalanches are irreversible, dissipative systems, minimizing – in space – entropy production. Furthermore, entropy production is linear both near and far from steady-state non-equilibrium because of the mass-continuity constraint. Finally, we derive thermodynamic forces and conjugate fluxes as well as expressing the corresponding phenomenological Onsager coefficients in terms of the constitutive parameters.

scholarly journals The maximum entropy production principle: two basic questions

2010 ◽  
Vol 365 (1545) ◽  
pp. 1333-1334 ◽  
Author(s):  
Leonid M. Martyushev
Keyword(s):  
Statistical Mechanics ◽  
Entropy Production ◽  
Maximum Entropy ◽  
Statistical Physics ◽  
Overwhelming Majority ◽  
Equilibrium Thermodynamics ◽  
Maximum Entropy Production ◽  
Environmental Systems ◽  
Thermodynamics And Statistical Mechanics ◽  
Non Equilibrium

The overwhelming majority of maximum entropy production applications to ecological and environmental systems are based on thermodynamics and statistical physics. Here, we discuss briefly maximum entropy production principle and raises two questions: (i) can this principle be used as the basis for non-equilibrium thermodynamics and statistical mechanics and (ii) is it possible to ‘prove’ the principle? We adduce one more proof which is most concise today.

scholarly journals Minimization of a free-energy-like potential for non-equilibrium flow systems at steady state

2010 ◽  
Vol 365 (1545) ◽  
pp. 1323-1331 ◽  
Author(s):  
Robert K. Niven
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Equilibrium Thermodynamics ◽  
Turbulent Fluid Flow ◽  
System A ◽  
Flow Heat ◽  
Observed Behaviour ◽  
New Formulation ◽  
Non Equilibrium

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the ‘maximum entropy production’ (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function ϕ st for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reductions in ϕ st arise from increases in the ‘flux entropy’ of the system—a measure of the variability of the fluxes—or in the local entropy production; conditionally, depending on the behaviour of the flux entropy, the formulation reduces to the MEP principle. The inferred steady state is also shown to exhibit high variability in its instantaneous fluxes and rates, consistent with the observed behaviour of turbulent fluid flow, heat convection and biological systems; one consequence is the coexistence of energy producers and consumers in ecological systems. The different paths for attaining steady state are also classified.

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