Controlling the environment in which we live has always been a human concern. Controlling an environment depends on analysis and predictions. To achieve this, researchers use mathematical models, which are created using differential and integral equations. At the present time, there are different types of differential and integrative factors, which can be categorised based on the concept of rate of change. They are mainly used to depict natural events after Markovian processes, processes that do not contain memory. Differential and integrative factors can be based on the nucleus of energy law, and these operators are used to capture natural events after energy law processes, and processes without a clear beginning and end. These problems can be found in many areas of science, technology, and engineering. The differentiation and integration operators with the law of exponential decay are used to depict processes such as fatigue, vanishing memory problems, and intersection with a stable state. Nature is full of such problems. Differential and integral operators with cross behaviour in thermoelasticity, quantum optics, and statistical mechanics are used to solve more complex problems, especially problems that follow two different processes including, for example, fading memory and the energy law. Finally, differential and integral operators with dual properties, for instance memory and self-similarities, constitute powerful mathematical tools used to model nature.

There have been many developments in physical applications by the great progress that scientists have made towards an ever-deepening understanding of the basic concepts of quantum physics, parallel to the beginning of quantum information technology and communications engineering. The ability to quantify, control, and manipulate quantum systems on an individual level is an essential pilot resource that can be exploited in all these areas of research represented by quantum measurements, quantum sensing and control, and quantum communication. Certainly, regarding the development of quantum technology, thermoelasticity, and statistical mechanics tools, the possibility of or not gaining the ability to deal with a large number of quantum entanglement states is being explored, which is a mandatory path to reach new heights in quantum information science. In the framework shown above, in which the physical applications in quantum mechanics are considered to have reached a significant stage of complete maturity, quantum optics and quantum information are still, as always, the vanguard.

The main aim of this Special Issue is to publish new original research and review articles that deal with phenomena related to thermoelasticity theory, quantum optics, statistical mechanics, nonlinear dynamics, fluid dynamics, differential equations, quantum information, semiconducting, and mathematical modelling. In addition, studies that make a comparison between these topics and their applications in diverse practical fields are welcome.

Potential topics include but are not limited to the following:

• Thermoelasticity theory
• Quantum optics
• Statistical mechanics
• Nonlinear dynamics
• Fluid dynamics
• Differential equations
• Quantum information
• Semiconducting
• Mathematical modelling