Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation

1992 ◽  
Vol 67 (3-4) ◽  
pp. 575-608 ◽  
Author(s):  
E. A. Carlen ◽  
M. C. Carvalho
Keyword(s):  
Boltzmann Equation ◽  
Rate Of Convergence ◽  
Entropy Production ◽  
Convergence To Equilibrium ◽  
The Boltzmann Equation

scholarly journals On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

2009 ◽  
Vol 135 (4) ◽  
pp. 681-736 ◽  
Author(s):  
Eric A. Carlen ◽  
Maria C. Carvalho ◽  
Xuguang Lu
Keyword(s):  
Boltzmann Equation ◽  
Strong Convergence ◽  
Convergence To Equilibrium ◽  
The Boltzmann Equation

scholarly journals A Study of the Entropy Production in Physical Processes from a New Perspective of the Energy Structure

2020 ◽  
Vol 8 (6) ◽  
Author(s):  
Saeed Shahsavari ◽  
Mehran Moradi
Keyword(s):  
Boltzmann Equation ◽  
Entropy Production ◽  
Physical Process ◽  
Structure Equation ◽  
Dissipated Energy ◽  
Energy Structure ◽  
Physical Processes ◽  
Physical Systems ◽  
The Boltzmann Equation ◽  
Energy Components

When a physical process is performed, identifying the generated entropy can be used to investigate the irreversibility. But for this mean, from the perspective of the Boltzmann equation, both all microstates and macrostates must be studied. In fact, it is needed that all particles energy level to be investigated. Therefore, to investigate entropy in configurationally systems using the Boltzmann equation, a very large volume of calculations is required. In this study, we try to extract a way to investigate entropy production without the need to study all particles (or sub-structures). For this purpose, at first, a macroscopic energy structure equation “as an equation that shows the energy components of the system activated in the performed process as well as their dependence” is presented. As a study on the irreversibility (or entropy production) in physical systems, its structure and components are studied. Writing equations in the energy space of the system makes it possible to study the structure of irreversibility. Then using a new macroscopic quasi-statistical approach, the irreversibility and its structure in physical processes are investigated. Macro energy components of the system are used for this investigation and energy structure is studied base on them. Finally, a new macroscopic definition of the generated entropy is extracted using a new energy structure equation as well as dependent and independent macroscopic energy component concepts. Also, why and what entropy can be generated, from the perspective of the presented macroscopic energy structure equation are studied. In fact, this paper investigates the generated entropy structure in physical systems using macroscopic system energy components and takes a new approach to why and what irreversibility is occurred during the physical process. Therefore, presented equations can be used for investigating the irreversibility in configurationally physical systems without the need to study all its sub structures. Also, from the extracted equations, it can be concluded that entropy is generated because of the existence of the dependent energy components in the energy structure equation of the system, and this generated entropy depends on the variation of these components as well as the amount of the applied energy to the system and its conditions. Due to the kinematic theory of dissipated energy, these results are in the same line with the different formulations of the second law of thermodynamics.  

Sign in / Sign up

Export Citation Format

Share Document