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oai:figshare.com:article/34023840 2026-09-29T16:10:52Z category_30151 item_type_12 month_year_09_2026

Exact memory requirements for retaining path irreversibility in finite Markov systems Satoshi Kawasaki (24726982) Thermodynamics and statistical physics stochastic thermodynamics coarse-graining path irreversibility exact coding Markov jump processes memory requirements <p dir="ltr">Coarse-graining can preserve a dynamical task while losing the irreversibility of a realized trajectory. We study the additional information that must remain after labeled jumps have been read and discarded, so that the accumulated path log-likelihood ratio can be reconstructed exactly and updated under subsequent inputs. For a fixed product of homogeneous three-state rings with positive rational rates and a uniform stationary initial law, this question reduces to an integer-current coding problem. Given the total jump count m, and no other history-dependent side information, the exact number of required output classes is C_E(m) = |E S_d(m)|, where E is the prime-exponent matrix of the rate ratios and S_d(m) is the reachable current set. If r = rank_Q E, the minimum additional fixed-length code uses r log₂(m+1) + O_E(1) bits. A recursive counter representation attains this leading term. For two rationally independent logarithmic affinities, we construct an exact recursive code for the (m+1)² classes. Established relative-entropy identities place these results within coarse-grained stochastic thermodynamics and separate realized-value retention from preservation of mean dissipation or fluctuation statistics. The bounds concern a conditional representation with a symbolic output; event-count storage, working space, model constants, and physical implementation costs are separate. Exact finite checks support the constructions but do not replace the proofs.</p><p><br></p><p dir="ltr">This item contains the preprint PDF and a reproducibility archive with manuscript sources, unchanged finite-check code, expected outputs, and verification instructions.</p> 2026-09-29T16:10:52Z Text Preprint 10.6084/m9.figshare.34023840.v1 https://figshare.com/articles/preprint/Exact_memory_requirements_for_retaining_path_irreversibility_in_finite_Markov_systems/34023840 CC BY 4.0