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Iirr(tc)=1−h2 ⁣(1−Dirr(tc)2)I_{\rm irr}(t_c)= 1-h_2\!\left(\frac{1-D_{\rm irr}(t_c)}{2}\right)

Why this formula appears here

The infimum asks how little path distinguishability remains after the best allowed attempt to erase it. For equal priors, an associated unavoidable decision information is Iirr(tc)=1−h2 ⁣(1−Dirr(tc)2)I_{\rm irr}(t_c)= 1-h_2\!\left(\frac{1-D_{\rm irr}(t_c)}{2}\right). Finally, the proposed horizon receipt time is

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IirrI_{\rm irr}

Symbol I_rm irr

IrI_rm irr is part of the quantity the equation computes from the expression on the right.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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Iirr(tc)=1−h2 ⁣(1−Dirr(tc)2).I_{\rm irr}(t_c)= 1-h_2\!\left(\frac{1-D_{\rm irr}(t_c)}{2}\right).

Equation 43 · Evolutionary Physics

How Fast Can a Horizon Learn Which Path You Took?

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The infimum asks how little path distinguishability remains after the best allowed attempt to erase it. For equal priors, an associated unavoidable decision information is Iirr(tc)=1−h2 ⁣(1−Dirr(tc)2)I_{\rm irr}(t_c)= 1-h_2\!\left(\frac{1-D_{\rm irr}(t_c)}{2}\right). Finally, the proposed horizon receipt time is

Meanings in this article

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