Entropy Is an Interface: Reversibility in the Substrate, Irreversibility at Commit
Recognition Physics Institute, Austin, Texas, USA
Summary
Entropy is defined operationally as a codelength at a declared measurement channel. A channel is specified by a coarse‑graining window $W:X\!\to Z$ and a noise/response kernel $K(y\mid z)$; the observable distribution is $p_Y(y)=\int K(y\mid W(x))\,d\mu(x)$. The interface entropy is $S_{W,K}(\mu)=L^*(p_Y)$ (optimal prefix‑free length). Reversible micro‑evolution that leaves $p_Y$ unchanged conserves $S_{W,K}$; commits (writes/binnings/erasures) increase it by data‑processing. Landauer work cost attaches to erasure as code‑length increments.
Abstract
This interface view recovers textbook entropies (Gibbs/Boltzmann/Shannon) as special cases, predicts how reported entropy depends lawfully on the chosen $(W,K)$, and resolves Maxwell‑demon accounting: irreversibility is the bill paid at commit, not a defect of the substrate. The paper gives a methods‑first protocol—declare $(W,K)$, compute $S_{W,K}$ as codelength, and report entropy production as code‑length increments across commits—and illustrates archival demonstrations (blackbody spectra, atomic line lists, quasi‑static gas processes). The framework is falsifiable: any reproducible decrease of $S_{W,K}$ across a commit without exported negentropy would refute it.
Key Contributions
- Operational definition: $S_{W,K}(\mu)=L^*(p_Y)$ at a declared channel
- Arrow at commits: reversible micro‑steps conserve $S$; commits increase $S$
- Landauer mapping: $W_{\min}\ge k_B T\ln2\cdot\Delta S$ with $\Delta S$ measured in bits at the channel
- Archival demos: blackbody, gas processes, atomic spectra; preregistered channels and scoring
- Falsifiers: commit violations; interface invariance; alignment tests