Maximisation of the entropy in non-equilibrium

Abstract:In the last two decades, the Maximum Entropy Principle (MEP) has been successfully employed to construct macroscopic models able to describe the charge and heat transport in semiconductor devices. These models are obtained, starting from the Boltzmann transport equations, for the charge and the phonon distribution functions, by taking-as macroscopic variables-suitable moments of the distributions and exploiting MEP in order to close the evolution equations for the chosen moments. Important results have also been obtained for the description of charge transport in devices made both of elemental and compound semiconductors, in cases where charge confinement is present and the carrier flow is two-or one-dimensional.

Section: The 3d Semiclassical Macroscopic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploitation of the Maximum Entropy Principle in Mathematical Modeling of Charge Transport in Semiconductors

Mascali

Romano

2017

“…Recent results have shown that the procedure of MEP for the closure of the moments equations for rarefied gases, complies with the recent macroscopic approach of extended thermodynamics to real and perfect gases [33][34][35].…”

Section: Introductionmentioning

confidence: 56%

“…An alternative method for achieving the closure of the system of equations is provided by MEP, which has its roots in statistical mechanics and information theory [31,32,94]. Originally motivated by the similarity of RET and moment equations derived from the Boltzmann equation on one hand, and by the observation made by Kogan [95] according to which the Grad's distribution function maximizes the entropy on the other hand, MEP was first proposed by Dreyer [35], then generalized by Müller and Ruggeri to the case of any number of moments [11], and later proposed again and popularized by Levermore [96]. More precisely, suppose to close the system (45) retaining the densities until the tensorial index N. We have the system of balance law…”

Section: Molecular Extended Thermodynamics Of Moments and Maximum Entmentioning

confidence: 99%

Entropy Principle and Recent Results in Non-Equilibrium Theories

Cimmelli

Jou

Ruggeri

et al. 2014

We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.

“…This idea of entropy maximization goes back to Jaynes [48,49], and is applied widely in information theory. In the kinetic theory of gases, this principle is applied in order to calculate higher order moments of the velocity distribution [50][51][52][53]. In the context of the mesoscopic theory, it has been applied in [47].…”

Section: Combination Of Mesoscopic and Macroscopic Descriptionsmentioning

confidence: 99%

Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals

Papenfuß

Muschik

2018

Internal and mesoscopic variables differ fundamentally from each other: both are state space variables, but mesoscopic variables are additionally equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of the liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as a mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers.