Quantum Corridor III: Generator-Level Relative-Entropy Dissipation and Unraveling-Invariant Irreversibility

Kenneth Searcy

Published Mar 10, 2026• 0 citations

Abstract

Irreversibility can be fixed before any path-space choice is made. This paper is the third quantum installment in the Forced Structure Series. It begins from the results of Quantum Corridor I and Quantum Corridor II, where admissible noncommutative maps were fixed as completely positive trace-preserving maps, quantum relative entropy was fixed as the corridor divergence, and admissible continuous-time evolution was fixed in the GKSL/Lindblad semigroup setting. The central result of the present paper is that these earlier corridor commitments already determine an intrinsic generator-level quantity: the instantaneous decay rate of the relative entropy D(Phi_t(rho)||pi) along an admissible semigroup Phi_t = e^(tL) relative to a faithful stationary state pi. In finite dimension, for strictly positive initial states, this rate is shown to equal -Tr(L(rho)(log rho - log pi)), and it is therefore nonnegative. The quantity is generator-determined and independent of any unraveling or path-space realization. In the commuting limit, it reduces to the classical generator-level entropy production rate. The paper is explicit about scope: it proves a canonical generator-level relative-entropy dissipation rate, not a full thermodynamic characterization, not a complete equality condition, and not yet a path-space bridge theorem.

DOI: 10.5281/zenodo.18942863

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