Abstract
The problem of understanding entropy and irreversibility has been tackled by thousands of physicists during the past century. Schools of thought have formed and flourished around different perspectives of the problem. But a definitive solution has yet to be found.1
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References
For recent reviews of the problem, see: R. Jancel, Foundations of Classical and Quantum Statistical Mechanics, Pergamon Press, Oxford, 1969; A. Wehrl, Rev. Mod. Phys., Vol. 50, 221 (1978); O. Penrose, Rep. Mod. Phys., Vol. 42, 129 (1979); J.L. Park and R.F. Simmons, Jr., in Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology, ed. A. van der Merwe, Plenum Press, 1983.
G.P. Beretta, Thesis, MIT, 1981, unpublished.
G.P. Beretta, E.P. Gyftopoulos, J.L. Park and G.N. Hatsopoulos, Nuovo Cimento B, Vol. 82, 169 (1984).
G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol. 6, 15, 127, 439, 561 (1976).
Throughout this lecture we proceed heuristically and disregard all questions of purely technical mathematical nature.
E.T. Jaynes, Phys. Rev., Vol. 106, 620 (1957); Vol. 108, 171 (1957).
Here D (F) is the domain of definition of function F, which does not necessarily coincide with the set S
Equilibrium solution ρe is stable according to Liapunoff if and only if for every ɛ > 0 there is a δ (ɛ) > 0 such that any solution ρ (t) with | | ρ (0) - ρe | | < δ (ɛ) remains with | | ρ (t) - ρe | | < ɛ for every t > 0, where | | • | | denotes the norm on L defined by | | A | | = (A | A).
G.P. Beretta, Int. J. Theor. Phys., Vol. 24, 119 (1985).
G.P. Beretta, to be published.
G.P. Beretta, E.P. Gyftopoulos and J.L. Park, Nuovo Cimento B, in press.
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© 1986 Plenum Press, New York
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Beretta, G.P. (1986). A General Nonlinear Evolution Equation for Irreversible Conservative Approach to Stable Equilibrium. In: Moore, G.T., Scully, M.O. (eds) Frontiers of Nonequilibrium Statistical Physics. NATO ASI Series, vol 135. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2181-1_14
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