Unitary Entities Are the True "Atoms"

Quantitative Geometrical Thermodynamics (QGT) exploits the entropic Lagrangian-Hamiltonian canonical equations of state as applied to entities obeying the holographic principle and exhibiting Shannon information, the creation of which measures the (validly defined) "entropic purpose" of the system. QGT provides a physical description for what we might consider the true "atoms" of physical science and has also recently enabled a number of significant advances: accounting ab initio for the chirality of DNA and the stability of Buckminsterfullerene; the size of the alpha particle (and other nuclear entities) and the lifetime of the free neutron; and the shape, structure, and stability of the Milky Way galaxy. All these entities, ranging in size over more than 38 orders of magnitude, can each be considered to be an "atom"; in particular, the size of the alpha is calculated from QGT by assuming that the alpha is a "unitary entity" (that is, than which exists no simpler). The surprising conclusion is that clearly compound entities may also be physically treated as unitary ("uncuttable") according to a principle of scale relativity, where a characteristic size for such an entity must be specified. Since QGT is entropic, and is therefore described using a logarithmic metric (involving hyperbolic space), it is not surprising that the length scale must be specified in order to account for unitary properties and for an entity to be appropriately considered an "atom". The contribution to physics made by QGT is reviewed in the context of the related work of others.