Analysis of a Plastic Collision to Determine the Mass of a Bit

Abstract

The possibility that information measured in bits has an associated equivalent mass has been argued by Vopson, who relied on Landauer’s principle, leading to the mass-energy-information equivalence principle. This principle states that the mass of a bit stored in classical digital memory at 300 K is on the order of \(3.19 \times {{10}^{{ - 38}}}~\) kg, implying that a 1 TB device must increase its mass by \(2.5 \times {{10}^{{ - 25}}}~\) kg to move from the erased state to the full digital information state. Similarly, in this work, we explore how an ideal gas can increase its mass owing to an increase in its entropy, based on the fact that information and entropy are related by an identity. Specifically, we have established that when one mole of an ideal gas changes its temperature from 50 to 4000 K, its entropy content increases by \(5.71 \times {{10}^{{24}}}\) bits, while its mass increases by \(5.47 \times {{10}^{{ - 13}}}~\) kg. These calculations reaffirm the possibility that information is the fifth state of matter and that the mass-energy-information equivalence principle is correct.