IDA-MACROSYSTEMS. STATE PROBABILITIES AND EQUILIBRIUM STATES
Authors:
Type:
Article
Pages:
from 192
to 196
Status:
Published
Received:
29.08.2014
Accepted:
06.10.2014
Published:
06.10.2014
Language:
Russian
Keywords:
macroscopic systems, Young diagrams, neighbourhood
Abstract (English):
We consider a new model of macroscopic systems whose microscopic states are given by Young diagrams. A new metric is introduced at the set of Young diagrams with the same number of cells, so that macroscopic states of the systems are defined as unit neighbourhoods of the microscopic ones. This allows to assign to each Young diagram a certain probability proportional to its neighbourhood capacity. We obtain explicit formulas for unit neighbourhood capacities of 2D and 3D Young diagrams and investigate the properties of equilibrium diagrams – diagrams with maximum neighbourhood capacity.
We consider a new model of macroscopic systems whose microscopic states are given by Young diagrams. A new metric is introduced at the set of Young diagrams with the same number of cells, so that macroscopic states of the systems are defined as unit neighbourhoods of the microscopic ones. This allows to assign to each Young diagram a certain probability proportional to its neighbourhood capacity. We obtain explicit formulas for unit neighbourhood capacities of 2D and 3D Young diagrams and investigate the properties of equilibrium diagrams – diagrams with maximum neighbourhood capacity.
Keywords:
macroscopic systems, Young diagrams, neighbourhood
macroscopic systems, Young diagrams, neighbourhood
Разбиение есть представление числа в виде суммы невозрастающих слагаемых. Графическим изображением разбиения служит диаграмма Юнга – таблица из клеток, каждая строка которой соответствует части разбиения.
