scholarly journals On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 204 ◽  
Author(s):  
Shu-Nan Li ◽  
Bing-Yang Cao
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Power Series Expansion ◽  
Irreversible Thermodynamics ◽  
Entropy Density ◽  
Transport Equations ◽  
Entropy Production Rate ◽  
Boltzmann Transport ◽  
Relaxation Time Approximation ◽  
Entropy Flux

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects.

scholarly journals Fractional-order heat conduction models from generalized Boltzmann transport equation

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190280 ◽  
Author(s):  
Shu-Nan Li ◽  
Bing-Yang Cao
Keyword(s):  
Heat Conduction ◽  
Entropy Production ◽  
Production Rate ◽  
Fractional Order ◽  
Mean Square Displacement ◽  
Linear Response Theory ◽  
Entropy Density ◽  
Entropy Production Rate ◽  
Boltzmann Transport ◽  
Entropy Flux

The relationship between fractional-order heat conduction models and Boltzmann transport equations (BTEs) lacks a detailed investigation. In this paper, the continuity, constitutive and governing equations of heat conduction are derived based on fractional-order phonon BTEs. The underlying microscopic regimes of the generalized Cattaneo equation are thereafter presented. The effective thermal conductivity κ eff converges in the subdiffusive regime and diverges in the superdiffusive regime. A connection between the divergence and mean-square displacement 〈|Δ x | 2 〉 ∼  t γ is established, namely, κ eff  ∼  t γ −1 , which coincides with the linear response theory. Entropic concepts, including the entropy density, entropy flux and entropy production rate, are studied likewise. Two non-trivial behaviours are observed, including the fractional-order expression of entropy flux and initial effects on the entropy production rate. In contrast with the continuous time random walk model, the results involve the non-classical continuity equations and entropic concepts. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

scholarly journals It is not the entropy you produce, rather, how you produce it

2010 ◽  
Vol 365 (1545) ◽  
pp. 1317-1322 ◽  
Author(s):  
Tyler Volk ◽  
Olivier Pauluis
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Thought Experiment ◽  
Biological Evolution ◽  
Irreversible Thermodynamics ◽  
Entropy Production Rate ◽  
Chemical Systems ◽  
Principle Of Maximum Entropy ◽  
Relative Contribution ◽  
Principle Of Maximum

The principle of maximum entropy production (MEP) seeks to better understand a large variety of the Earth's environmental and ecological systems by postulating that processes far from thermodynamic equilibrium will ‘adapt to steady states at which they dissipate energy and produce entropy at the maximum possible rate’. Our aim in this ‘outside view’, invited by Axel Kleidon, is to focus on what we think is an outstanding challenge for MEP and for irreversible thermodynamics in general: making specific predictions about the relative contribution of individual processes to entropy production. Using studies that compared entropy production in the atmosphere of a dry versus humid Earth, we show that two systems might have the same entropy production rate but very different internal dynamics of dissipation. Using the results of several of the papers in this special issue and a thought experiment, we show that components of life-containing systems can evolve to either lower or raise the entropy production rate. Our analysis makes explicit fundamental questions for MEP that should be brought into focus: can MEP predict not just the overall state of entropy production of a system but also the details of the sub-systems of dissipaters within the system? Which fluxes of the system are those that are most likely to be maximized? How it is possible for MEP theory to be so domain-neutral that it can claim to apply equally to both purely physical–chemical systems and also systems governed by the ‘laws’ of biological evolution? We conclude that the principle of MEP needs to take on the issue of exactly how entropy is produced.

scholarly journals Local detailed balance

2021 ◽  
Author(s):  
Christian Maes
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Physical Meaning ◽  
Detailed Balance ◽  
Entropy Production Rate ◽  
Central Concept ◽  
Fluctuation Relations ◽  
Entropy Flux ◽  
The Mean

We review the physical meaning and mathematical implementation of the condition of local detailed balance for a class of nonequilibrium mesoscopic processes. A central concept is that of fluctuating entropy flux for which the steady average gives the mean entropy production rate. We repeat how local detailed balance is essentially equivalent to the widely discussed fluctuation relations for that entropy flux and hence is at most ``only half of the story.''

scholarly journals Entropy Production Rate for Avascular Tumor Growth

2011 ◽  
Vol 02 (06) ◽  
pp. 615-620 ◽  
Author(s):  
Elena Izquierdo-Kulich ◽  
Esther Alonso-Becerra ◽  
José M Nieto-Villar
Keyword(s):  
Tumor Growth ◽  
Entropy Production ◽  
Production Rate ◽  
Entropy Production Rate ◽  
Avascular Tumor

scholarly journals Measurement of entropy production rate in compressible turbulence

2006 ◽  
Vol 76 (4) ◽  
pp. 595-601 ◽  
Author(s):  
M. M Bandi ◽  
W. I Goldburg ◽  
J. R Cressman
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Compressible Turbulence ◽  
Entropy Production Rate

scholarly journals Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 881 ◽  
Author(s):  
Karl Hoffmann ◽  
Kathrin Kulmus ◽  
Christopher Essex ◽  
Janett Prehl
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Irreversible Processes ◽  
Entropy Production Rate ◽  
Continuous Space ◽  
One Dimensional ◽  
Fractional Diffusion Equations ◽  
And Diffusion

The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a finite chain of points described by a fractional master equation.

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