The origin of irreversibility

Did the analysis in Section 9.1 demonstrate irreversibility It should be emphasized that while the dynamics of the system is completely reversible, as implied by the underlying equations of motion, the appearance of irreversibility has resulted from the particular question asked. This section focuses on understanding this and other aspects of quantum irreversibility. 

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We have shown that the origin of irreversibility in dynamics comes from Poincare s non-integrability. It is well known that Poincare introduced a fundamental distinction between integrable and non-integrable systems. Briefly, in integrable systems you can eliminate interactions. Then you come to a situation of independent objects which can be integrated easily. But as Poincare already... 

Jean Bricmont [1995], professor of theoretical physics at the Catholic University at Louvain — a short distance from Brussels — believes that Prigogine s philosophical conclusions are not supported by his results in statistical mechanics, and that his interpretations are seriously misleading. Bricmont s main point is that Boltzmann s late-nineteenth-century explanation of the origin of irreversibility is fully satisfactory. On this basis recent work on the thermodynamics of irreversible processes has not brought about radical change in fundamental physical understanding. Bricmont states ... 

Prigogine and his coworkers considered that their results from these several research initiatives were mutually reinforcing — and that their most recent research definitely established that the origin of irreversibility is local rather than global in character. 

A simple model that illustrates the mathematical origins of irreversibility was first introduced by Kac in 1956 [kac56] and has come to be known as Kac s Ring Model. 

The irreversibility of Te electrodeposition is increased by changing the tellurite solution to pH 10, Figure 9C. At pH 10, the potential difference between deposition and stripping for the 1/1 couple is 600 mV. The origin of peak 0 is still unclear, but appears to be due to changes in an adsorbed layer of tellurium oxide. 

Chracteristics of B. m terium s plasmid system have been summarized by Carlton (3p. The plasmids are typical in that they band as covalently closed circular DNA in ethidium bromide-cesium chloride gradients and they are resistant to irreversible alkaline denaturation (17). However, B. megaterium plasmids are atypical in that they exist in approximately 10 size classes and as many copies per cell ( ). In fact, for the smaller plasmids there are hundreds of copies per cell so that plasmid DNA may represent up to 40% of the total extractable DNA (31). This is unusual since for most plasmids there are usually no more than a few copies per cell. Also, hybridization studies suggest that there is extensive homology between three B. megaterium plasmids of different sizes and between these plasmids and the chromosomal DNA (31,33). Carlton (31) concludes that the most likely explanation of the origin of B. megaterium plasmids is that they are molecular hybrids between one or more plasmid elements and various portions of the chromosomal DNA. 

As shown in Table 1, the amount of irreversibly adsorbed pyridine dropped to one third its original value after modification, which is caused by the methylation of surface Bronsted acidic sites through equation (1). The results were confirmed by the presence of surface methoxyl groups and the absence of Bpy peaks of adsorbed pyridine in i.r. spectra. The TPD of ammonia in Figure 3 indicates that the modification influenced mainly the number of surface acidic sites. The results in Table 1 aslo show that the drop in acidity paralleled that... 

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