# Entropy : Zero 2 _HOT_

We examine ergodicity and configurational entropy for a dilute pigment solution and for a suspension of plant photosystem particles in which both ground and excited state pigments are present. It is concluded that the pigment solution, due to the extreme brevity of the excited state lifetime, is non-ergodic and the configurational entropy approaches zero. Conversely, due to the rapid energy transfer among pigments, each photosystem is ergodic and the configurational entropy is positive. This decreases the free energy of the single photosystem pigment array by a small amount. On the other hand, the suspension of photosystems is non-ergodic and the configurational entropy approaches zero. The overall configurational entropy which, in principle, includes contributions from both the single excited photosystems and the suspension which contains excited photosystems, also approaches zero. Thus the configurational entropy upon photon absorption by either a pigment solution or a suspension of photosystem particles is approximately zero.

## Entropy : Zero 2

Let us explain data supplied in Table 1. Row 1 supplies the general data related to the basic Marjorie Rice Tiling 11. Small letters (a, b, c) denote edges of the tiling; capitals (A, B, C) denote angles of the tiling. Row 2 of the table depicts the modifications of Tiling 11; row 3 supplies the values of edges and angles for various modifications of Tiling 11. Row 4 depicts the corresponding pentagons, constituting Tiling 11. Row 5 depicts the Voronoi diagrams generated by the vertices of various modifications of Tiling 11. Row 6 supplies the values of the Shannon entropy and parameter Î¶ defined by Equation (2). The types of polygons appearing in the Voronoi diagram are also presented in row 6. Angles, denoted B, C, D, and E, inherent for Tiling 11, enable variation within [140;158], [80;44], [130;112], [100;136], respectively. Edges a, b, and c also enable variation in the flexible Marjorie Rice Tilling 11.

Quantitative parameters of the set of Voronoi tessellations emerging from the 15 basic pentagons. The types of basic pentagons are supplied in Table A1. The values the Shannon entropy and parameter Î¶ defined by Equation (2) and quantifying the ratio of polygon types which are present in the given tessellation are supplied.

Obviously, the Shannon entropy of the source tessellation built of pentagons only is zero. It is recognized that the Shannon entropy of the Voronoi tessellations is varied in a broad range for the mosaics emerging from the same source pentagonal tiling, namely Equation (3) is true for Tiling 11: 041b061a72