Canonical ensemble of open strings



The integral equation has been received for the probability density of distance r between the ends of the string with the preset length L. This equation is invariant under the continuous group of renormalization transformations that initiated using the renormalization method to search out the required probability density asymptotic. The ensemble of such strings with any lengths is considered, and the canonical distribution probability density of distance is established. The results presented can be used to determine the entropy of nanostructures, thereby their thermodynamics in condition monitoring is established.

Общая информация

Ключевые слова: Open string, canonical ensemble, entropy

Рубрика издания: Научная жизнь

Тип материала: научная статья

Для цитаты: Алхимов В.И. Canonical ensemble of open strings // Моделирование и анализ данных. 2012. Том 2. № 1. С. 92–96.

Полный текст



The result obtained can be used as a purely theoretical study of various systems as well as in technical applications. In particular, by using the formula (13), the entropy of nanostructures can be determined, thereby their thermodynamics in condition monitoring is established. This result allows to establish criterion for the strength of chain systems, depending on the physical state of their environment.


  1. Alkhimov V.I., “Configuration statistics of the open string d-dimensional model”, Modelling and data analysis, 2011, No 1, pp 41 -54 (in Russian).
  2. Huang K., “Statistical mechanics”, John Wiley & Sons, Inc.: N.Y.–London, 1963.
  3. Bateman H., Erdelyi A., “Higher transcendental functions”, Vol 2, Mc Graw-Hill Book Comp. Inc.: N.Y.–London, 1953.

Информация об авторах

Алхимов Валерий Иванович, доктор физико-математических наук, профессор кафедры прикладной математики факультета информационных технологий, ФГБОУ ВО МГППУ, Москва, Россия, e-mail:



Всего: 801
В прошлом месяце: 1
В текущем месяце: 1


Всего: 396
В прошлом месяце: 0
В текущем месяце: 0