Statistical theory of diffusion-limited growth in two dimensions

Yoshinori Hayakawa, Shinichi Sato

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    A formalism of irreversible aggregation processes is presented in terms of statistical mechanics. Thermodynamical variables that include the degeneracy of the histories, which we call “history entropy,” are introduced by taking into account all possible growth histories. By considering the thermodynamic properties of the growth history and harmonic measure, we find the condition of the most probable history for diffusion-limited aggregation (DLA) as a function of mass fractal dimension of the resulting clusters. Families of fractal growth generators are utilized for the estimation of the history entropy, and the fractal dimension of observable DLA clusters in two dimensions is evaluated in accordance with numerical and experimental results.

    Original languageEnglish
    Pages (from-to)95-98
    Number of pages4
    JournalPhysical review letters
    Issue number1
    Publication statusPublished - 1997

    ASJC Scopus subject areas

    • Physics and Astronomy(all)


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