Einstein crystals in Snyder and Snyder-de Sitter noncommutative backgrounds

We investigate the behavior of Einstein crystals in noncommutative backgrounds described by the Snyder and Snyder-de Sitter models. Possible novel effects, which may arise in realistic systems such as diamond crystals, are analyzed within a thermodynamical framework. We show that noncommutativity influences the key thermodynamic quantities, including internal energy and specific heat. These corrections can be directly related to modifications of the underlying uncertainty relations, of the generalized uncertainty principle (GUP) and generalized extended uncertainty principle (GEUP) types.