Griffith theory of physical fractures, statistical procedures and entropy production: Rosetta stone's legacy.

A physical model, based on energy balances, is proposed to describe the fractures in solid structures such as stelae, tiles, glass, and others. We applied the model to investigate the transition of the Rosetta Stone from the original state to the final state with three major fractures. We consider a statistical corner-breaking model with cutting rules. We obtain a probability distribution as a function of the area and the number of vertices. Our generic results are consistent with the current state of the Rosetta Stone and, additionally, predictions related to a fourth fracture are declared. The loss of information on such heritage pieces is considered through entropy production. The explicit quantification of this concept in information theory stays examined.

Configurations of Proto-Cell Aggregates with Anisotropy: Gravity Promotes Complexity in Theoretical Biology.

This contribution considers proto-cell structures associated with asymmetries, mainly gravity, in the framework of reaction-diffusion. There are equivalent solutions for defined morphogen parameters in the equations that allow for defining proto-tissue complexity and configurational entropy. Using RNA data, improvements to the complexity and entropy due to the Earth's gravity are presented. The theoretical proto-tissues complexity estimation, as a function of arbitrary surface gravity, is likewise proposed. In this sense, hypothetical aggregates of proto-cells on Mars would have a lower complexity than on Earth, which is equally valid for the Moon. Massive planets, or exoplanets like BD+20594b, could have major proto-tissue complexity and, eventually, rich biodiversity.

Prebiotic Aggregates (Tissues) Emerging from Reaction-Diffusion: Formation Time, Configuration Entropy and Optimal Spatial Dimension.

For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of information and alike traits, is characterized by the number of equivalent patterns conferring viability against selection processes. In the case of structural parameters and the diffusion coefficient of ribonucleic acid, the formation time ranges between a few years to some decades, depending on the spatial dimension (fractional or not). As long as equivalent patterns exist, the configuration entropy of proto-tissues can be defined and used as a practical tool. Consequently, the maximal diversity and weak fluctuations, for which proto-tissues can develop, occur at the spatial dimension 2.5.

Entropy Signature for Crack Networks in Old Paintings: Saturation Prospectus.

In desiccated films, particularly with old paintings, molecular bonds may break to create intricate patterns of macroscopic cracks. The resulting directions of the cracks quantifiably enable an evaluation of the entropy and degree of disorder in the network. Experimental tests on prepared samples and a two-interacting-variables model allow the evolution of entropy to be tracked. Calculations were performed, primarily using data from the painting Girl with a Pearl Earring by Vermeer, revealing that the left side of the girl's face features a crack structure with higher entropy (or less order) than the right side. Other old paintings were considered. The extrapolation of experiments to these old paintings confirms that saturation still is not reached.