Principle of minimum loss of Fisher information, arising from the Cramer-Rao inequality: Its role in evolution of bio-physical laws, complex systems and universes

Abstract A thermodynamically open system ordinarily obeys physical laws expressing maximum randomness. How, then, do real systems grow in ordered complexity, information content and size? Consider an “information channel”: this is a closed system, acting as a channel linking a vital input of information to an output device. An example is a cell membrane (CM) receiving vital input information about its environment, as carried by, say, an entering K+ ion. The information channel extends radially through the thickness of that CM; into the cell cytoplasm just beyond it. The total passage of the ion from input to output channel also describes a physical signal carrying Fisher information (FI) in the form of a charge current p(t) in time. Providing this information to the cell allows it to grow in complexity, and survive. During this time the CM is otherwise closed to inputs. It cannot receive any additional environmental information. Then, any change in the information so-carried can only be a loss. On the other hand, the growth in complexity of any well-defined system increases linearly with its (Fisher) information level. Hence the cell's growth in complexity is maximized if the information level is maximized (obeys an MFI principle); or equivalently, if the above loss of channel information is minimized. As shown, thanks to the Cramer-Rao inequality, this MFI principle holds widely, normally over all time for all material channels. Such channels consist of evolving systems: sub-nuclear particles, quantum particles, classical particles, biological viruses such as the coronavirus, cells, plants, animals, economic systems, sociological systems, planets, galaxies and universes. Mathematically, demanding MFI (formerly termed “extreme physical information” or EPI) of a physical system yields a differential equation defining its probability law p(x) = a⁎(x) ∙ a(x), x = x, y, z, ct, through a real, complex or tensor amplitude law a(x), q(x), Ψ(x) or Ψ(xα), xα = x, y, z, ct, respectively. Its outcomes x are randomly sampled during system use and evolution. The system is predicted to obey properties of continued, evolutionary growth and complexity (organization). Because each grows independently, to achieve even higher values of FI it splits off (give “birth to”) a subsidiary that continues evolving via MF. This is independent of its “parent” system, so their FI values can maximally add. In biology, a parent (plant, or animal, …) gives rise to an offspring. In economics, a parent company splits off a subsidiary. In cosmology, a universe splits off an “offspring” universe. The offspring universe so forms, and evolves independent of its parent, as required, when located in an incomplete vacuum (containing a finite, yet small, number of molecules/cubic meter). Even the most nearly perfect vacuum in intergalactic space obeys this property. To further satisfy the EPI requirement of maximized total Fisher (MFI) a large number of such universes Un, n = 1, …, N,called a “multiverse,” independently form. Each can exist, and evolve on its own, since each obeys the same 26 universal physical constants as ours. The formation of universe Un initiates only after Un − 1 ships phenomena, identifying the 26 constants, to it. These are via a narrow Lorentz wormhole channel within Un − 1, stretching from its interior, to just outside its “bubble” surface. There a point P of incomplete vacuum is assumed to exist, allowing universe Un to start evolving. Effects encouraging or inhibiting or (even) annihilating such created universes are discussed.