The paper studies the possibility of unifying the two branches of the irreversible engineering THERMODYNAMICS, namely finite physical dimensions THERMODYNAMICS (FPDT) and finite speed THERMODYNAMICS (FST), aiming to take into account their benefits and successes and to eliminate as much as possible their disadvantages. Actually, the two branches have the same goal, that of optimizing the performance of thermal machines and they were developed almost in parallel. Analysis of thermal machines cycles using the FPDT is based on the first and second law of THERMODYNAMICS, in the presence of the external irreversibility generated by the heat transfer at finite temperature difference at the thermal reservoirs and internal irreversibility, using the internal source of entropy considered as parameter or function to be specified. The FST is based on the mathematical expression of the first law for process with finite speed that involves three causes of internal irreversibility, namely the finite speed of the piston, internal friction and throttling. The direct method is used in the analysis of thermal machines cycles to provide analytical expression of the machine performance (efficiency and power) as a function of the speed of the process. The significant progress of these two branches of irreversible engineering THERMODYNAMICS makes their unification a desirable outcome. We hope that the new model yielded from this study will provide an even more important tool for engineers that will help their attempt to a better design and optimization of thermal machines.

On the basis of the theory of THERMODYNAMICS, a new formalism of classical nonrelativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on a (1+n) -dimensional smooth manifold are geometrically treated as dynamical variables. The statistical mechanics of particle trajectories are constructed in a classical manner. Thermodynamic variables are introduced through a partition function based on a canonical ensemble of trajectories. Within this theoretical framework, classical mechanics can be interpreted as an equilibrium state of statistical mechanics. The relationship between classical and quantum mechanics is discussed from the viewpoint of statistical mechanics. The maximum-entropy principle is shown to provide a unified view of both classical and quantum mechanics.

This research paper presents a critical study of the ‘Rational irreversible THERMODYNAMICS’ framework on evaluating its theoretical foundations and practical applications. A comprehensive review of existing framework and theoretical analysis has been carried out. We identify the principles, assumptions, and limitations inherent in rational irreversible THERMODYNAMICS. Our findings highlight discrepancies between theoretical predictions and experimental observations, particularly in highly non-equilibrium systems. The critical evaluation presented in this study elucidates the challenges and opportunities in rational irreversible THERMODYNAMICS, leading the way for future research.

In this paper, we delve into the thermodynamic topology of AdS Reissner-Nordström (R-N) black holes by employing nonextensive entropy frameworks, specifically Rényi (with nonextensive parameter $\lambda$) and Sharma-Mittal entropy (with nonextensive parameter $\alpha, \beta$). Our investigation spans two frameworks: bulk boundary and restricted phase space (RPS) THERMODYNAMICS. In the bulk boundary framework, we face singular zero points revealing topological charges influenced by the free parameter $(\lambda)$ with a positive topological charge $(\omega = +1)$ and the total topological charge $(W = +1)$, indicating the presence of a single stable on-shell black hole. Further analysis shows that when $(\lambda)$ is set to zero, the equations align with the Bekenstein-Hawking entropy structure, demonstrating different behaviors with multiple topological charges $(\omega = +1, -1, +1)$. Notably, increasing the parameter $\alpha$ in Sharma-Mittal entropy results in multiple topological charges $(\omega = +1, -1, +1)$ with the total topological charge $(W = +1)$. Conversely, increasing $(\beta)$ reduces the number of topological charges, maintaining the total topological charge $(W = +1)$. Extending our study to the restricted phase space, we observe consistent topological charges $(\omega = +1)$ across all conditions and parameters. This consistency persists even when reducing to Bekenstein-Hawking entropy, suggesting similar behaviors in both non-extended and Hawking entropy states within RPS.

The stability constants, free energies, enthalpies and entropies of 1:1 complex formation between triphenyltin chloride as a Lewis acid and chloride, bromide and iodide as Lewis bases were measured spectrophotometrically. The stability constant trend as well as the thermodynamic parameter trend are in accord with the softness increase, i.e., Cl- < Br- < I-, which shows that triphenyltin chloride behaves as a soft acid.

The anionic surfactant sodium n-dodecyl sulfate (SDS) plays a variety of roles with regard to protein conformation, depending on its concentration. SDS at low concentrations mostly induces the compaction of protein (folding). Examples of this include: the molten globule state of acid-unfolded cytochrome c, associated with enhancement of the exothermic enthalpy values of isothermal titration calorimetry and a reversible profile by differential scanning calorimetry; the enzyme activation and compaction of Aspergillus niger catalase, and relationship of calorimetric enthalpy (D Hcal) to van’t Hoff enthalpy (D HVH), which proves the existence of intermolecular and intramolecular interaction during enzyme activation by SDS; the production of a new energetic domain for human apotransferrin and folded state for histone H1 by SDS. SDS at moderate concentrations below the critical micelle concentration (cmc) is a potent denaturant for protein in solution. Protein denaturation is a key method in THERMODYNAMICS and binding site analysis and can be used to enhance our understanding of the protein structure-function relationship. The interaction between protein and surfactant, such as SDS, at the cmc level is a complicated interaction, thermodynamically, that should bring about enthalpy correction through micellar dissociation and micelle dilution.