#jxxcarlson:landauerstheorem #folder:quantumcomputing
The connection between Shannon entropy and physics was initially unclear.
But thanks to advances in stochastic thermodynamics, the Landauer principle is now understood to be a direct consequence of the second law of thermodynamics, which states that entropy production \(\Sigma\) never decreases.
For a system exchanging heat with a reservoir, \(\Sigma = \Delta S + Q/T\), where \(\Delta S\) is the system’s change in entropy during some process and \(Q\) is the resulting heat released. The second law of thermodynamics reads \(\Sigma \ge 0\). Erasing information on a classical bit corresponds to changing the Shannon entropy from its maximal value of \(k_B \ln 2\) to its smallest value 0, for an entropy change of \(-k_B \ln 2\). Thus \(-k_B \ln 2 + Q/T \ge 0\), so that
|| equation Q k_B T
[bold Preskill:] Rolf Landauer pointed out in 1961 that erasure of information is necessarily a [underline dissipative] process. His insight is that erasure always involves the compression of phase space and so is irreversible. For example, I can store one bit of information by placing a single molecule in a box, either on the left side or the right side of a partition that divides the box. Erasure means that we move the molecule to the left side, say, irrespective of whether it started out on the left or right. I can suddenly remove the partition and then slowly compress the one molecule “gas” with a piston until the molecule is defnitely on the left side. This procedure reduces the entropy of the gas by \(\Delta S = k \ln 2\) and there is an associated flow of heat from the box to the environment. If the process is isothermal at temperature \(T\), then work \(W = kT \ln 2\) is performed on the box — work that I have to provide. If I am to erase information someone will have to pay the power bill.
Landauer’s principle UMD slides
The Physics of Information: From Maxwell to Landauer
Experimental Verification of Landauer’s Principle (Rutgers)
Physical Foundations of Landauer’s Principle (Frank)
Less Wrong: On Landauer’s Principle
Boltzmann Distribution (Chem Libre)
Carnot engine as a two-phase power cycle (MIT)