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We discuss a nonlinear model for the relaxation by energy redistributionwithin an isolated, closed system composed of non-interacting identicalparticles with energy levels e_i with i=1,2,...,N. The time-dependentoccupation probabilities p_i(t) are assumed to obey the nonlinear rateequations tau dp_i/dt=-p_i ln p_i+ alpha(t)p_i-beta(t)e_ip_i where alpha(t) andbeta(t) are functionals of the p_i(t)'s that maintain invariant the mean energyE=sum_i e_ip_i(t) and the normalization condition 1=sum_i p_i(t). The entropyS(t)=-k sum_i p_i(t) ln p_i(t) is a non-decreasing function of time until theinitially nonzero occupation probabilities reach a Boltzmann-like canonicaldistribution over the occupied energy eigenstates. Initially zero occupationprobabilities, instead, remain zero at all times. The solutions p_i(t) of therate equations are unique and well-defined for arbitrary initial conditionsp_i(0) and for all times. Existence and uniqueness both forward and backward intime allows the reconstruction of the primordial lowest entropy state. The timeevolution is at all times along the local direction of steepest entropy ascentor, equivalently, of maximal entropy generation. These rate equations have thesame mathematical structure and basic features of the nonlinear dynamicalequation proposed in a series of papers ended with G.P.Beretta, Found.Phys.,17, 365 (1987) and recently rediscovered in S. Gheorghiu-Svirschevski,Phys.Rev.A, 63, 022105 and 054102 (2001). Numerical results illustrate thefeatures of the dynamics and the differences with the rate equations recentlyconsidered for the same problem in M.Lemanska and Z.Jaeger, Physica D, 170, 72(2002).Comment: 11 pages, 7 eps figures (psfrag use removed), uses subeqn, minor  revisions, accepted for Physical Review

Nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution