We derive the distribution function and the allied thermodynamic quantities for a system of galaxies with three mass species. A new clustering parameter b 3 that inherently takes into account the masses and the number of galaxies of each kind, emerges directly from the calculations. Our general conclusion is that the inclusion of the third component does not significantly effect the overall features of the distribution function.

In this work, we investigate the implications of the concept of quantum speed limit in string field theory. We adopt a novel approach to the problem of time on world-sheet based on Fisher information, and arrive at a minimum time for a particle state to evolve into another particle state. This is done using both the Mandelstam-Tamm bound and the Margolus-Levitin bound. This implies that any interaction has to be smeared over such an interval, and any interaction in the effective quantum field theory has to be non-local. As non-local quantum field theories are known to be finite, it is expected that divergences should be removed from effective quantum field theories due to the quantum speed limit of string theory.

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