Is There A Connection Between A 2X2 Matrix Model Of The Energy Momentum Equation And Statistical Mechanics?
Francesco R. Ruggeri
A 2x2 matrix model of Einstein´s energy momentum equation appears to have links to statistical mechanics. First, it seems to suggest using dp (change in momentum) as a constant when counting energy levels in statistical mechanical calculations of the partition function. It also has further links to the de Broglie wavelength which is used to justify the use of equally spaced dp for energy state counting. It also appears that a 2x2 matrix model is consistent with Knuth´s statistical model. The two component positive energy eigenvector represents square roots of forward and backward motion probabilities. These probabilities maximize entropy. Thus, it appears that the 2x2 model, which uses quantum mechanical formalism, is also equivalent to a statistical mechanical model. In other words, at least in this model, there appears to be a link between statistical mechanics and quantum mechanics . It should be noted, however, that in this note very little has been shown about this link other than the equivalency of the energy eigenvector with maximum entropy. It is also suggested that zitterbewegung could lead to statistical fluctuations and that they may account for issues in statistical mechanics when interparticle separations reach the size of the de Broglie wavelength.
•Apr 11, 2018•0 citations