Summary
The existence of the Boltzmann equation and its generalizations is studied by analysing the order of magnitude of their terms. As a consequence we conclude that the reduced distribution functions are not analytic in the density.
Riassunto
Si studia l'esistenza dell'equazione di Boltzmann e delle sue generalizzazioni analizzando l'ordine di grandezza dei loro termini. In conseguenza si conclude che le funzioni di distribuzioni ridotte non sono analitiche nella densità.
Резюме
Исследуется существование уравнения Больцмана и его обобщений, посредством анализа порядка величины членов этих уравнений. Вследствие этого мы заключаем, что приведенные функции распределения не являются аналитическими по плотности.
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References
J. R. Dorfman andE. G. D. Cohen:Journ. Math. Phys.,8, 282 (1967) and references quoted therein.
K. Kawasaki andI. Oppenheim:Phys. Rev.,136, A 1519 (1964);139, A 1763 (1965);J. Albers andI. Oppenheim:Physica,59, 161, 187 (1972).
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P. Mazur andJ. Biel:Physica,32, 1633 (1966).
J. Biel andJ. Marro:Nuovo Cimento,20 B, 25 (1974).
Cf. eq. (22) of ref. (4).
Cf. eqs. (20) and (24) of ref. (5).
Cf. eq. (24) of ref. (4).
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Biel, J., Marro, J. & Navarro, L. On the existence of kinetic equations. Nuovo Cim 20, 55–63 (1974). https://doi.org/10.1007/BF02721106
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DOI: https://doi.org/10.1007/BF02721106