PostulateStatement: Literature-sourcedProof: Not applicablePipeline-generated‡ sources checked 2026-10-15

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Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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Finite bath kernels preserve the stage canonical law

Physical scope

The transition matrices of the specified finite-state model preserve each stage's canonical probability vector; no universal Markov approximation or physical thermalization theorem is asserted.

Postulate

For the protocol in Finite driven protocol and path work, adopt, at each stage $k = 1, \dots, m$ , the stationarity condition $\sum_{i \in Ω} π_{k} (i) K_{k} (i, j) = π_{k} (j)$ for every $j \in Ω$ . This says that if the bath transition begins with law $π_{k}$ at fixed energy $E_{k}$ , it ends with the same law. It is a physical modeling assumption for this protocol family, not a consequence of the transition-kernel definition and not an assertion that the kernel mixes every initial law to $π_{k}$ .

Depends on

Finite driven protocol and path work

Finite bath kernels preserve the stage canonical law

Postulate

Depends on

Dependency tree · 2 levels

Sources