Paramacrosystems with arrangement

Abstract

Parastatistical macroscopic classical systems with distinguishable states (cells) and arranged state occupation (IDA-systems) are considered. In one-dimensional case (IDA1-systems) they are shown to be equivalent to the systems with indistinguishable elements and states (II-systems). In two-dimensional case (IDA2-systems) they require special approach. Their microscopic states are associated with one- and two-dimensional Young diagrams, respectively. Macroscopic states are defined as neighbourhoods of microscopic ones. Explicit expressions for probabilities and entropies of macroscopic states are derived. Analysis of equilibrium states reveals shell-type mechanism of growth for IDA-systems.