Reproduction code — When can maximum entropy production select a branch? Frenesy, quasi-potentials, and closure conditions

Reproduction code and outputs for the manuscript "When can maximum entropy production select a branch? Frenesy, quasi-potentials, and closure conditions" (S. Kaneko). The manuscript shows that maximum entropy production (MEP) is not a universal branch-selection principle: branch selection is governed by the full contracted path action, of which entropy production is only the time-antisymmetric part, and the omitted time-symmetric activity (frenesy) can reverse the dissipation ordering. This package reproduces every numerical result of the paper and its Supplemental Material (SM), in three groups. (1) Core finite-state results, deterministic and seed-free: the two exact finite-state Markov counterexamples (Theorems 1 and 2), the edgewise local-detailed-balance checks, the single-gate cut-balance exactness checks, and the driven-ring lemma. These regenerate the two published main-text figures and every diagnostic value quoted in the text. (2) Stochastic Boussinesq illustration (SM Sec. S3): a 2D stochastic Rayleigh-Benard quench and a fixed-Rayleigh-number ensemble scan producing the deposited Boussinesq diagnostic figures and machine-readable summaries. The diagnostic Sigma(t) = integral |grad T|^2 dA is an output only; the update rules contain no optimizer, no argmax, and no maximum-entropy path ensemble (anti-teleological check). (3) Pseudo-spectral DNS for SM Sec. S7, new in V4, in spectral_RB_DNS/: an executed pseudo-spectral direct-numerical-simulation notebook testing whether a sheared convective mean flow self-sustains in 2D Boussinesq Rayleigh-Benard convection (the "anti-MEP" scenario). Across Ra <= 1e5, aspect ratio Gamma in {2,4}, and Prandtl number Pr in {0.05,1}, no self-sustaining mean flow is found: a seeded shear either decays or fires a single transient relaxation-oscillation burst (suppressing the heat flux by up to about 85% at Ra = 1e5) before the higher-dissipation gradient-roll state is recovered. A sustained low-dissipation sheared branch requires high Ra, small Gamma, and Pr >~ 3, a structural closure condition consistent with the paper's no-go result. The package is self-contained, with the executed Colab notebook for groups (1)-(2), the executed DNS notebook for group (3), the standalone Python scripts, the figures, and machine-readable summaries. Version history: V4 adds the DNS package for SM Sec. S7 in spectral_RB_DNS/, all earlier files retained unchanged; V3 contained the finite-state counterexamples, cut-balance checks, driven-ring lemma, and the Boussinesq illustration (SM Sec. S3). The manuscript and SM cite this dataset by its concept DOI (10.17632/pgstrtnwj8), which always resolves to the latest version. Licensing: the scripts and notebooks are under the MIT License; the DNS data files and figures in spectral_RB_DNS/ are under CC BY 4.0 (see the LICENSE files). For scholarly reuse, cite this dataset DOI together with the manuscript.本数据集为论文《最大熵产生何时可选择分支？Frenesy、拟势与闭合条件》（原标题：When can maximum entropy production select a branch? Frenesy, quasi-potentials, and closure conditions，作者S. Kaneko）的复现代码与输出结果。该论文指出，最大熵产生（Maximum Entropy Production, MEP）并非普适的分支选择准则：分支选择由完整的约化路径作用量支配，熵产生仅为其中的时间反演不对称部分，而被忽略的时间对称活性（frenesy）可反转耗散序。本代码包分为三组，可复现论文及其补充材料（Supplemental Material, SM）中的全部数值结果。 (1) 核心有限态结果（确定性、无种子初始化）：两个精确有限态马尔可夫反例（定理1与定理2）、逐边局域细致平衡校验、单门割平衡精确性校验，以及驱动环引理。本部分可复现论文正文中的两张已发表主图，以及正文中引用的全部诊断数值。 (2) 随机布辛涅斯克（Boussinesq）模拟示例（补充材料S3节）：包含二维随机瑞利-贝纳德（Rayleigh-Bénard）淬火实验，以及固定瑞利数系综扫描程序，可生成布辛涅斯克诊断图与机器可读摘要。其中诊断量Σ(t) = ∫|grad T|² dA仅作为输出生成；更新规则未包含任何优化器、argmax操作，亦未采用最大熵路径系综（反目的论校验）。 (3) 补充材料S7节的伪谱直接数值模拟（Pseudo-spectral Direct Numerical Simulation, DNS）（V4版本新增，位于spectral_RB_DNS/目录下）：该可执行伪谱直接数值模拟笔记本用于检验二维布辛涅斯克瑞利-贝纳德对流中，剪切对流平均流是否能够自维持（即"反最大熵产生"场景）。在瑞利数（Rayleigh number, Ra）≤ 1e5、长宽比（aspect ratio, Γ）∈{2,4}、普朗特数（Prandtl number, Pr）∈{0.05,1}的参数范围内，未发现自维持的平均流：预置剪切流要么发生衰减，要么触发单次瞬态弛豫振荡脉冲（在Ra=1e5时可将热通量抑制约85%），随后系统恢复至高耗散梯度卷状态。维持低耗散剪切分支需要高瑞利数、小长宽比以及Pr ≳ 3，该结构闭合条件与论文的禁戒结果一致。 本代码包具备自包含性，包含可执行的(1)-(2)组代码的Colab笔记本、(3)组的可执行DNS笔记本、独立Python脚本、生成的图片，以及机器可读摘要。版本历史：V4版本于spectral_RB_DNS/目录下新增了补充材料S7节的DNS代码包，其余原有文件未做修改；V3版本包含有限态反例、割平衡校验、驱动环引理以及布辛涅斯克模拟示例（补充材料S3节）。论文及补充材料通过概念DOI（10.17632/pgstrtnwj8）引用本数据集，该DOI始终指向最新版本。许可协议：脚本与笔记本采用MIT License；spectral_RB_DNS/目录下的DNS数据文件与图片采用CC BY 4.0许可协议（详见LICENSE文件）。若用于学术再利用，请同时引用本数据集DOI与原论文。