Information theory and thermal properties of an extended cosine hyperbolic potential model

This study presents the information-theoretic measures and molar thermodynamic properties for an extended cosine hyperbolic potential. The analytic expressions for the Fisher information in both position and momentum spaces are derived. The Shannon entropy for both position and momentum spaces are also derived. The Cramér-Rao bound and Beckner-Bialynicki-Birula-Mycielski (BBM) inequality are tested and confirmed, presenting the model as a good fit for the study of information theory. The study of thermodynamic properties is applied to phosphorus (P₂), potassium (K₂), potassium bromide (KBr), and silicon monoxide (SiO) molecules using specific analytical equations. The results for molar enthalpy (H), molar entropy (S), molar Gibbs free energy (G), and molar heat capacity (Cp) for the four molecules across a temperature range of 0 K to 6000 K are numerically obtained. The predicted results demonstrate excellent consistency with experimental data obtained from the National Institute of Standards and Technology (NIST) database. The discrepancies observed indicate minor variations in the model’s accuracy, providing reliable predictions for the molar thermodynamic properties of the molecules. The performance of the model validates its suitability for studying information theory and accurately representing thermal properties.