Equations
The universal form of the bound was originally found by Jacob Bekenstein as the inequality
where S is the entropy, k is Boltzmann's constant, R is the radius of a sphere that can enclose the given system, E is the total mass-energy including any rest masses, ħ is the reduced Planck constant, and c is the speed of light. Note that while gravity plays a significant role in its enforcement, the expression for the bound does not contain Newton's Constant G.
In informational terms, the bound is given by
where I is the information expressed in number of bits contained in the quantum states in the sphere. The ln 2 factor comes from defining the information as the logarithm to the base 2 of the number of quantum states. The right-hand side of the foregoing relation is approximately equal to 2.5769087×1043×(mass in kilograms)×(radius in meters).
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