Abstract
A recurrent probabilistic-bit (p-bit) neuron with a given temporal response can keep its memory in two places: a retained analog state or feedback through its own stochastic output bit. Both give the same expected response to every input and the same read count, but not the same noise. With independent reads, the retained-state placement has the smallest state distribution in convex order at every finite horizon, and the exact stationary variance ratio reaches 39 at response pole 0.95 with one read per update; 324 simulated cells confirm the exact moments. We then take the reads from a telegraph-correlated stochastic magnetic tunnel junction (sMTJ) model with read interval r0 = Δt/τcorr in zero-bias correlation times. An exact moment recursion for the bias-independent device class is confirmed on 720 cells; the Arrhenius class is simulated. Correlated reads break the matched response, erode the penalty from 39 to 5.8 at r0 = 0.25 and shift the feedback endpoint's mean for Arrhenius devices, but no tested cell reversed the variance ordering beyond Monte Carlo error. The rule r0 ≥ ln [A(2+ε)/ε] keeps a bias-independent-class integrator within a fraction ε of its fresh-read noise and is conservative for Arrhenius devices.