Joint Landauer and Bekenstein Bound: Minimum Volume for a Heat-Limited Memory

This paper examines what smallest volume can hold a memory whose erasure heat and whose information content are both respected. The calculation is performed in a frame with a finite maximum density, the neutron-branch value rho_A = 9.718e+57 kg per cubic metre, with the electron branch at 2.874e+51 kg per cubic metre for comparison. Headline results include a bounce temperature of 3.278e+22 K, a Landauer cost at that temperature of 3.137e-01 J per bit against 2.871e-21 J per bit at 300 K, a Bekenstein allowance of 1.049e+94 bits for the stated centimetre reference region, and a Margolus-Levitin rate of 2.209e+103 per second for the same region. The two conditions cross at a definite volume for each stated temperature, and below that volume at least one of the two bounds is breached. All numbers are computed from the stated assumptions in the accompanying script; the study is simulated and computed, not measured.