4. Irreversible evolution

2018 ◽  
pp. 125-146
Author(s):  
Olivier Darrigol

This chapter covers Boltzmann’s writings about the Boltzmann equation and the H theorem in the period 1872–1875, through which he succeeded in deriving the irreversible evolution of the distribution of molecular velocities in a dilute gas toward Maxwell’s distribution. Boltzmann also used his equation to improve on Maxwell’s theory of transport phenomena (viscosity, diffusion, and heat conduction). The bulky memoir of 1872 and the eponymous equation probably are Boltzmann’s most famous achievements. Despite the now often obsolete ways of demonstration, despite the lengthiness of the arguments, and despite hidden difficulties in the foundations, Boltzmann there displayed his constructive skills at their best.


Author(s):  
Sauro Succi

Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous H-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underlying microdynamics.


2004 ◽  
Vol 97-98 ◽  
pp. 77-84
Author(s):  
Juras Ulbikas ◽  
Liudas Leonas ◽  
Daiva Ulbikienė ◽  
Stepas Janušonis

Self-formation as a concept for irreversible evolution of the artificial object with complexity increase was introduced for understanding of the processes existing in microelectronics technology [1]. The concept of self-formation by itself was to some extend influenced by principles existing in biological world therefore from the very beginning there was an open question about limits of self-formation application: are we limited to the understanding of some technological processes or we can think about predicting new technological applications by applying selfformation concept. Recently developed tools for simulation of technological processes for Solar Cells manufacturing [2] clearly indicates that self-formation is becoming interesting tool for technologists trying to create and optimize microelectronic devices. The next step exploring selfformation application boundaries can be analysis of possibilities of the self-formation to demonstrate usual in biological life development and reproduction of the object. This presentation will be dedicated to the analysis of the conditions and possibilities by applying self-formation present self-formation, development and reproduction of artificial object.


Author(s):  
Yuanlin Xu ◽  
Chen Wang ◽  
Yu Shi ◽  
Guoxing Miao ◽  
Jing Fu ◽  
...  

We identify that the irreversible evolution of flat to nonuniform topography on the pristine Zn anode surface during the repeated stripping/plating cycles triggers the fatal dendrite growth. Given this, a...


2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Karla Costa ◽  
Jamson Nunes Junior ◽  
Guilherme Giunzioni ◽  
Maria de Fatima Rizzo ◽  
Gabriela Paladini

We present here a case of Fahr’s disease in the pediatric age group. Fahr’s disease is a neurological, degenerative and rare disease, especially in this age group. It differs from Fahrs syndrome, which is associated with infectious pathologies, such as human immunodeficiency virus infection and metabolic causes, such as hypoparathyroidism. In contrast, Fahr’s disease has an idiopathic or familial cause and is related to neuropsychic symptoms. However, the differentiation of these terms is still poorly established in the literature. It has an unknown prevalence and affects individuals of both sexes in any age group, and individuals from the 4th decade are more likely to develop it. It has polygenic etiology being autosomal dominant, characterized by abnormal deposits of minerals, including mainly calcium and phosphate in the basal ganglia. It presents extra-pyramidal, psychiatric and epileptic manifestations. It is an incurable disease with progressive and irreversible evolution. Due to the involvement of the central nervous system, the prognosis is reserved and eventually fatal. The patient in question was MF, 15-years-old, male, with severe holocranial headache and convulsive crisis with findings of calcifications in the base ganglia bilaterally tomography of the skull.


Sign in / Sign up

Export Citation Format

Share Document