ENTROPY IN NONLINEAR QUANTUM-MECHANICS .2.

Regarding the discussion of Peres and Weinberg concerning a suitable definition of entropy in nonlinear quantum mechanics, two further observations are made. Firstly, by regarding the covariance matrix of the probability distribution over the phase space of wavefunctions as the nonlinear counterpart (rho(NL)) of the (linear) density matrix (rho(L)) and employing -Tr rho(NL) ln rho(NL), one obtains a limiting transition (as nonlinearities vanish), in which this entropy measure converges to the definition in ordinary quantum mechanics, -Tr rho(L) ln rho(L). Secondly, it is argued that Peres' contention that 'nonlinear variants of Schrodinger's equation violate the second law of thermodynamics' is flawed in that it relies upon the entropy of mixing of non-orthogonal states, which as Dieks and van Dijk have indicated is an undefined concept. A proper approach to associating a quantum mechanical entropy with a mixture of a particle into two non-orthogonal states- by first estimating a suitable two-particle density matrix (rho) and then employing -Tr rho ln rho-is outlined.