We reconsider the classical 1 bit absorption model of black hole (BH) growth as a discrete recursion rather than a continuum equation. Here “1 bit” denotes one elementary absorption unit in natural logarithmic units. For a Schwarzschild-Tangherlini BH, the discrete treatment yields the expected area scaling together with a logarithmic correction whose coefficient is fixed by the dimensional dependence of the mass step. We then extend the construction to the Reissner-Nordström case at fixed charge and show that the logarithmic coefficient acquires an explicit charge dependence. The fixed charge sector can be read as the asymptotic neutral growth stage after a charged seed has already been formed, so realistic charged absorption affects the initial cutoff rather than the large-mass recursion for weakly charged final states. Ordered charged, oppositely charged, and neutral labels define a formal history ensemble. In a unitary description, two different histories may lead to the same reduced macroscopic state $(M,Q,S)$ while remaining different in hidden or environmental degrees of freedom. Adding a mass or energy label reduces the end point degeneracy, but it does not remove it in the ensembles studied here. The corrected interpretation separates dynamical entropy, state entropy, history entropy, and hidden conditional entropy. It also clarifies that the multinomial formula is a restricted history-counting result rather than a proof of unique or identical microscopic BH states.

Close

PrevNext

View figure in article

• Classical black holes
• Entropy
• Entropic sampling methods