Fluctuation theorem for entropy production during effusion of a relativistic ideal gas

A modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye–Hückel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments hr1…rm(m) by means of the irreducible tensorial Hermite polynomials.

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Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

Physical Review E ◽

10.1103/physreve.60.2721 ◽

1999 ◽

Vol 60 (3) ◽

pp. 2721-2726 ◽

Cited By ~ 1426

Author(s):

Gavin E. Crooks

Keyword(s):

Free Energy ◽

Entropy Production ◽

Fluctuation Theorem

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Modeling of Entropy Production in Turbulent Flows

Journal of Fluids Engineering ◽

10.1115/1.1845551 ◽

2004 ◽

Vol 126 (6) ◽

pp. 893-899 ◽

Cited By ~ 39

Author(s):

O. B. Adeyinka ◽

G. F. Naterer

Keyword(s):

Entropy Production ◽

Turbulent Flows ◽

Incompressible Flows ◽

Momentum Equation ◽

Ideal Gas ◽

Equation Modeling ◽

Mean Flow ◽

Ideal Gas Law ◽

Empirical Relations ◽

Entropy Transport

This article presents new modeling of turbulence correlations in the entropy transport equation for viscous, incompressible flows. An explicit entropy equation of state is developed for gases with the ideal gas law, while entropy transport equations are derived for both gases and liquids. The formulation specifically considers incompressible forced convection problems without a buoyancy term in the y-momentum equation, as density variations are neglected. Reynolds averaging techniques are applied to the turbulence closure of fluctuating temperature and entropy fields. The problem of rigorously expressing the mean entropy production in terms of other mean flow quantities is addressed. The validity of the newly developed formulation is assessed using direct numerical simulation data and empirical relations for the friction factor. Also, the dissipation (ε) of turbulent kinetic energy is formulated in terms of the Second Law. In contrast to the conventional ε equation modeling, this article proposes an alternative method by utilizing both transport and positive definite forms of the entropy production equation.

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A note on acoustic turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.523 ◽

2019 ◽

Vol 874 ◽

Cited By ~ 2

Author(s):

Erik Lindborg

Keyword(s):

Structure Function ◽

Entropy Production ◽

Acoustic Field ◽

Three Dimensional ◽

Weak Shock ◽

Separation Distance ◽

Ideal Gas ◽

Order Structure ◽

Specific Heats ◽

The Mean

We consider a three-dimensional acoustic field of an ideal gas in which all entropy production is confined to weak shocks and show that similar scaling relations hold for such a field as for forced Burgers turbulence, where the shock amplitude scales as $(\unicode[STIX]{x1D716}d)^{1/3}$ and the $p$th-order structure function scales as $(\unicode[STIX]{x1D716}d)^{p/3}r/d$, $\unicode[STIX]{x1D716}$ being the mean energy dissipation per unit mass, $d$ the mean distance between the shocks and $r$ the separation distance. However, for the acoustic field, $\unicode[STIX]{x1D716}$ should be replaced by $\unicode[STIX]{x1D716}+\unicode[STIX]{x1D712}$, where $\unicode[STIX]{x1D712}$ is associated with entropy production due to heat conduction. In particular, the third-order longitudinal structure function scales as $\langle \unicode[STIX]{x1D6FF}u_{r}^{3}\rangle =-C(\unicode[STIX]{x1D716}+\unicode[STIX]{x1D712})r$, where $C$ takes the value $12/5(\unicode[STIX]{x1D6FE}+1)$ in the weak shock limit, $\unicode[STIX]{x1D6FE}=c_{p}/c_{v}$ being the ratio between the specific heats at constant pressure and constant volume.

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Thermodynamic Merger of Fluctuation Theorem and Principle of Least Action: Case of Rayleigh–Taylor Instability

Journal of Non-Equilibrium Thermodynamics ◽

10.1515/jnet-2018-0091 ◽

2019 ◽

Vol 44 (4) ◽

pp. 363-371

Author(s):

Shripad P. Mahulikar ◽

Tapan K. Sengupta ◽

Nidhi Sharma ◽

Pallavi Rastogi

Keyword(s):

Entropy Production ◽

Entropy Generation ◽

Dissipative System ◽

Fluctuation Theorem ◽

Generation Rate ◽

Dissipative Systems ◽

Entropy Generation Rate ◽

Least Action ◽

Principle Of Least Action

AbstractEntropy fluctuations with time occur in finite-sized time-evolving dissipative systems. There is a need to comprehend the role of these fluctuations on the fluctuations-averaged entropy generation rate, over a large enough observation time interval. In this non-equilibrium thermodynamic investigation, the Fluctuation Theorem (FT) and Principle of Least Action are re-visited to articulate their implications for dissipative systems. The Principle of Maximum Entropy Production (MaxEP: the entropy generation rate of a dissipative system is maximized by paths of least action) is conceptually identified as the Principle of Least Action for dissipative systems. A Thermodynamic Fusion Theorem that merges the FT and the MaxEP is introduced for addressing the role of fluctuations in entropy production. It identifies “entropy fluctuations” as the “least-action path” for maximizing the time-averaged entropy production in a dissipative system. The validity of this introduced theorem is demonstrated for the case of entropy fluctuations in Rayleigh–Taylor flow instability.

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