English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The unknown amplitude law q(x) defining an observed effect may be found usingthe principle of Extreme Physical Information. EPI is derived as follows. Theobservations follow an information flow J --> I, with J the informationintrinsic to the source and I the Fisher information level in its data, obeying(i) I=4 Integral dx q' -squared. Here q'= dq/dx and p(x) = q(x)-squared is theprobability. It was previously shown, using L. Hardy's 5 axioms definingphysics, that I = max. Therefore, its variation (ii) delta I = 0. Note that Iis generic, obeying (i) for all source effects, whereas J is specific to theparticular effect. Hence, rather than having form (i), J obeys (iii) J =Integral dx j[q(x),s(x)] with j some function of its arguments and s(x) a knownsource, such as of mass, biological fitness, etc. Information I decreases underany irreversible operation such as measurement, so that I l.e. J or,equivalently, I = kJ where 0 l.e. k l.e. 1. Then the variation delta I = kdelta J so that property (ii) gives (iv) delta J = 0 as well. Then combining(ii) and (iv), delta(I - J) = 0. Or, I - J = L = extremum. What kind ofextremum? Eqs. (i) and (iii) give (v) L=4q'^2 - j[q(x),s(x)]. Differentiating(v), (d^2 L )/(dq'^2) = +8. Then by the Legendre condition the extremum is aminimum. The unknown source effect obeys (vi) I - J= minimum, EPI.

Derivation of Principle of Extreme Physical Information