This work repositions entropy and irreversibility from the perspective of finite operations, rather than treating them as intrinsic physical properties or purely probabilistic notions. Starting from diffusion and Brownian motion as concrete physical examples, the paper formulates irreversibility as a consequence of finite accessible correlation under limited operational control, rather than as a fundamental asymmetry of microscopic laws. Entropy is consequently reinterpreted as a residual quantity arising from correlations that cannot be operationally reconstructed. Within this framework, classical thermodynamic entropy, Shannon information entropy, and Landauer’s principle are shown to share a common operational structure. The analysis does not introduce new physical interactions or modify established dynamical equations; instead, it reorganizes the conceptual placement of entropy and irreversibility across physics, information theory, and operational descriptions. The scope of the paper is explicitly cross-disciplinary. While physical diffusion processes provide the primary grounding, the framework clarifies why irreversibility appears universally across measurement, computation, and macroscopic observation when operational accessibility is finite. The limits and falsifiability of the framework are clearly stated, and no claims of a unified or final theory are made. This paper is intended as a foundational, integrative reference within the broader Finite-Operation Theory series.
Koji Mochizuki (Mon,) studied this question.