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 A CYCLE DECOMPOSITION AND ENTROPY PRODUCTION FOR CIRCULANT QUANTUM MARKOV SEMIGROUPS

2013 ◽  
Vol 16 (02) ◽  
pp. 1350016 ◽  
Author(s):  
JORGE R. BOLAÑOS-SERVIN ◽  
ROBERTO QUEZADA
Keyword(s):  
Entropy Production ◽  
Production Rate ◽  
Detailed Balance ◽  
Steady States ◽  
Quantum Entropy ◽  
Entropy Production Rate ◽  
Markov Semigroups ◽  
Cycle Decomposition ◽  
Definition Of ◽  
Insight Into

We propose a definition of cycle representation for Quantum Markov Semigroups (QMS) and of Quantum Entropy Production Rate (QEPR) in terms of the ρ-adjoint. We introduce the class of circulant QMS, which admit non-equilibrium steady states but exhibit symmetries that allow us to compute explicitly the QEPR, gain a deeper insight into the notion of cycle decomposition and prove that quantum detailed balance holds if and only if the QEPR equals zero.

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 Reversibility and entropy production of inhomogeneous Markov chains

2006 ◽  
Vol 43 (04) ◽  
pp. 1028-1043 ◽  
Author(s):  
Hao Ge ◽  
Da-Quan Jiang ◽  
Min Qian
Keyword(s):  
Markov Chains ◽  
Entropy Production ◽  
Production Rate ◽  
Detailed Balance ◽  
Entropy Production Rate ◽  
State Spaces ◽  
Brownian Motors ◽  
Simple Version ◽  
Inhomogeneous Markov Chain ◽  
Time Periodic

In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems.

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 Reversibility and entropy production of inhomogeneous Markov chains

2006 ◽  
Vol 43 (4) ◽  
pp. 1028-1043 ◽  
Author(s):  
Hao Ge ◽  
Da-Quan Jiang ◽  
Min Qian
Keyword(s):  
Markov Chains ◽  
Entropy Production ◽  
Production Rate ◽  
Detailed Balance ◽  
Entropy Production Rate ◽  
State Spaces ◽  
Brownian Motors ◽  
Simple Version ◽  
Inhomogeneous Markov Chain ◽  
Time Periodic

In this paper we introduce the concepts of instantaneous reversibility and instantaneous entropy production rate for inhomogeneous Markov chains with denumerable state spaces. The following statements are proved to be equivalent: the inhomogeneous Markov chain is instantaneously reversible; it is in detailed balance; its entropy production rate vanishes. In particular, for a time-periodic birth-death chain, which can be regarded as a simple version of a physical model (Brownian motors), we prove that its rotation number is 0 when it is instantaneously reversible or periodically reversible. Hence, in our model of Markov chains, the directed transport phenomenon of Brownian motors can occur only in nonequilibrium and irreversible systems.

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
Sign in / Sign up

Export Citation Format

Share Document