2006/03/28 by Victor F. Los, Los, Victor F.
Physics and Astronomy · Earth and Planetary Sciences · #Statistical Mechanics and Entropy #Advanced Thermodynamics and Statistical Mechanics #Earthquake Detection and Analysis
paper · pdf · doi:10.48550/arxiv.cond-mat/0603770
By using a time-dependent operator converting a distribution function\n(statistical operator) of a total system under consideration into the relevant\nform, new exact nonlinear generalized master equations (GMEs) are derived. The\ninhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig\nGME and is suitable for obtaining both the linear and nonlinear evolution\nequations. To include initial correlations into consideration, this\ninhomogeneous nonlinear GME has been converted into the homogenous form by the\nmethod suggested earlier in [9], [10]. Obtained homogeneous nonlinear GME\ndescribes all stages of the (sub)system of interest evolution and influence of\ninitial correlations at all stages thereof. In contrast to homogeneous linear\nGMEs obtained in [9], [10], the homogeneous nonlinear GME is convenient for\ngetting both a linear and nonlinear evolution equations. The obtained nonlinear\nGMEs have been tested on the space inhomogeneous dilute gas of classical\nparticles. Particularly, a new homogeneous nonlinear equation describing an\nevolution of a one-particle distribution function at all times and retaining\ninitial correlations has been obtained in the linear in the gas density\napproximation. This equation is closed in the sense that all two-particle\ncorrelations (collisions), including initial ones, which contribute to\ndissipative and nondissipative characteristics of the nonideal gas are\naccounted for. Connection of this equation at the kinetic stage of the\nevolution to the Vlasov-Landau and Boltzmann equations is discussed.\n