DOI

We develop statistical mechanics for stochastic growth processes and apply it to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasistatic) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with simply connected domains occupied by gas. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with a free-particle propagator on an infinite-dimensional complex manifold with a Kähler metric.

Язык оригиналаанглийский
Номер статьи010103
ЖурналPhysical Review E
Том96
Номер выпуска1
DOI
СостояниеОпубликовано - 20 июл 2017

    Предметные области Scopus

  • Статистическая и нелинейная физика
  • Теория вероятности и статистика
  • Физика конденсатов

ID: 36351758