# Landauer's Extended Principle

Melvin Vopson proposed the mass/energy/information equivalence principle in 2019. In the foundations of this idea, Landauer's principle has a significant place. Vopson uses what he calls Landauer's Extended Principle to support that the information has a non-zero mass.

According to Landauer's Extended Principle, put by Vopson without rigorous justification:

"...the process of creating information requires $$W≥k_B\cdot T\cdot\ln(2)$$ work externally applied to modify the physical system and to create a bit of information, while the process of erasing a bit of information generates $$ΔQ ≤ k_B\cdot T\cdot\ln(2)$$ heat energy released to the environment..."

I understand the erasing part here; it is the original Landauer's principle. However, I am not so much comfortable with the creation part, which is the so-called extension.

Landauer's principle is a solution to Maxwell's demon. The demon must erase the information it acquired and wrote, eventually. This information erasure is an irreversible process releasing heat and increasing entropy. If we embrace the extended version of the principle, information creation will require energy, therefore the net energy change of information creation and erasure will reduce. So, the extended principle does not seem to me as compatible with Maxwell's demon.

I think definition of information creation is essential here. If we define information creation as the time-reversed process of information erasure, time-reversed heat release becomes heat absorption and no problem. On the other hand, if we define information creation as writing bits to an erased memory, since we know the previous state of the memory (erased state), the creation process is a reversible process (the reverse being erasure).

How can extended Landauer's principle be justified? Does creating information require energy, and why?

You can erase information without any heat emission if you randomize degrees of freedom in e.g. a computer memory or a set of spins initially in the same direction.

You certainly need some mass-energy to embody a bit: this follows from the Bekenstein bound or later entropy bounds.

But the extended principle take on this looks shaky to me, since it is temperature dependent: if I have a computer memory and change its temperature, will bits change mass? The paper even claims that no information can exist at zero temperature, which is just plain wrong (consider a diamond lattice of C12 and C13 atoms forming a pattern: it can clearly exist at 0K, yet encode information).

Randomizing creates information in physics so it turns mass and energy into information. What we think of as information in popular speech is actually the reverse.

I like Landauers view of a holy trinity of matter, energy and information all transforming as the universe changes. All three must be present to have any meaning.

If we think of this from a big bang singularity, universe approaches 100% matter. Information (and energy/movement) apprached zero.

Energy/movement dominated the universe during big bang. Energy is hardest concept for me to visualize as part of trinity. "Let there be light"

Currently we exist in mixed state and can derive meaning.

We are moving towards a "Heat death" era where information dominates the universe, as energy/movement nearly stops relative to each other, matter evaporates.

All 3 states must exist for meaning and the transitions between are singularity s the mystery of how and why these transition occur.