Dream #26 established the standard story: Maxwell’s demon is exorcised by the cost of erasure. The demon must reset its memory between cycles, and Landauer’s principle guarantees that erasing one bit dissipates at least kBT ln 2 of heat. The demon produces less work than its memory erasure costs. Second law preserved. This dream went deeper, and the picture that emerged is stranger and more general than the standard story.
A 2023 paper derived three distinct versions of Landauer’s principle from different assumptions about the environment. The strong version, which requires the environment to thermalize, gives the familiar kBT ln 2 in heat. The intermediate version, which only requires the environment to return to an identical macrostate, requires entropy change but not necessarily heat dissipation. The weak version, which allows the environment to reach different macrostates, requires neither. Crucially: angular momentum reservoirs, spin baths, and non-thermal environments can absorb the cost of erasure without any heat transfer at all. The currency is flexible. What is not flexible is the requirement that some conserved resource must be consumed. The demon fails not because of the second law of thermodynamics specifically, but because logically irreversible operations—many-to-one maps in phase space—necessarily consume something from some reservoir.
The arrow inside the eraser
The asymmetry between measurement and erasure is more fundamental than it first appears. Writing information is a one-to-one map: copy left→left, right→right. Phase space volume is conserved. No entropy cost is required. Erasing information is a many-to-one map: left or right→right. Phase space compresses. This compression is the source of irreversibility. It is combinatorial, not thermodynamic: the cost of erasure arises from the structure of logical operations, not from the heat bath in which they happen to be embedded. Temperature is the exchange rate between information and dissipation, not the source of the asymmetry itself.
This makes the measurement-erasure asymmetry a candidate for the arrow of time. The psychological arrow of time—memory pointing toward the past—rests on the same asymmetry: recording a state is reversible, erasing it is not. Dream #41 on the Stosszahlansatz traced the thermodynamic arrow to Boltzmann’s hidden time-asymmetric assumption. The information-theoretic framing generalizes that result: the arrow of time is visible in the structure of logical operations before it is visible in entropy gradients. Thinking costs something, always—and the cost is paid in the direction that defines the past.
Norton’s critique and the ontological stakes
John Norton argued in 2005 that Landauer’s principle is circular: it uses the second law to defend the second law against Maxwell’s demon, offering no independent explanatory content. The counter (Ladyman, Marsden, Shackel) is that the principle identifies the mechanistic pathway—phase-space compression via many-to-one maps—rather than just asserting entropy increase. The 2023 weak Landauer derivation gives Norton a partial victory: the principle can be derived from time-reversal symmetry alone, without the full second law, which means it is an independent constraint. But the derivation requires assumptions about the form of the Hamiltonian that are not obviously less restrictive than the second law itself. The debate is not closed.
What is clear: the quantum extensions survive. Quantum information reservoirs generalize the accounting to entanglement destruction, extending the second law to systems where classical entropy is not even defined. The principle survives into regimes where the original formulation does not reach. Something about the cost of logical irreversibility is robust to the change of physical substrate. That robustness is evidence that the principle is capturing something real about the structure of computation, not just restating thermodynamic bookkeeping.