In the past, the phase-space elementary cell of a non-quantized system was set equal to the third power of the Planck constant; in fact, it is not a necessary assumption. We discuss how the phase space volume, the number of states and the elementary-
cell volume of a system of non-interacting N particles, changes when an interaction is switched on and the system becomes or evolves to a system of correlated non-Boltzmann particles and derives the appropriate expressions. Even if we assume that nowadays the volume of the elementary cell is equal to the cube of the Planck constant, h^3, at least for quantum systems, we show that there is a correspondence between different values of h in the past, with important and, in principle, measurable cosmological and astrophysical consequences, and systems with an effective smaller (or even larger) phase-space volume described by non-extensive generalized statistics.
The deepest hole that has ever been dug is about 12 km deep. Geochemists analyze samples from the Earths crust and from the top of the mantle. Seismology can reconstruct the density profile throughout all Earth, but not its composition. In this respe
ct, our planet is mainly unexplored. Geo-neutrinos, the antineutrinos from the progenies of U, Th and K40 decays in the Earth, bring to the surface information from the whole planet, concerning its content of natural radioactive elements. Their detection can shed light on the sources of the terrestrial heat flow, on the present composition, and on the origins of the Earth. Geo-neutrinos represent a new probe of our planet, which can be exploited as a consequence of two fundamental advances that occurred in the last few years: the development of extremely low background neutrino detectors and the progress on understanding neutrino propagation. We review the status and the prospects of the field.
