The Physics of 'Spilt Water Will Not Return to the Tray'

I am sure you are all familiar with the saying, 'Spilt water will not return to the tray.' It is a proverb meaning that what has happened cannot be undone. The origin of this saying is said to come from a story where a wife who had left her husband saw that he had been promoted and pressed for a reconciliation. The man replied, 'Try putting the water spilt on the ground back onto the tray.' He used a natural phenomenon that cannot be reversed to make her understand that there would be no reconciliation. Although this is a proverb, it can also be seen as a phrase that suggests the clear arrow of time that exists in the natural world.

In physics, a phenomenon that cannot be reversed is called 'irreversibility.' It is the arrow of time that clearly distinguishes the past, present, and future. The mechanics that govern the motion of single-particle systems include Newtonian mechanics, the theory of relativity for regions close to the speed of light, and quantum mechanics where wave properties become prominent in microscopic systems. These physical systems are often thought to be the main players in physics. However, these fundamental equations do not explain the irreversibility that essentially governs our natural world. The academic discipline that expresses irreversibility is a completely separate framework that you are also studying, called 'thermodynamics.'

The most important physical object for understanding thermodynamics is the heat engine. For example, by filling a container with gas and moving a piston in and out or changing the external temperature, heat is converted into work. I believe you all know that due to the irreversibility that governs the natural world, the conversion efficiency from heat to work cannot exceed the Carnot efficiency.

is known to hold true. Here, <...> signifies the average over all possible parameter changes of the external world (called a heat bath). This equality reproduces the principle of maximum work if one uses a mathematical inequality called Jensen's inequality.   

In recent years, vigorous research has been conducted with both experimental and theoretical sides cooperating to deepen and develop thermodynamics, centered on such equalities. Furthermore, more recently, exploring how thermalization phenomena occur in quantum isolated systems—with experiments on cold atoms and collision experiments of heavy ions using large accelerators in mind—is also becoming a central topic in physics. The phenomenon of thermalization is also an important aspect of physics that explores a part of the physics of irreversibility. Additionally, regarding the physics of black holes, active discussions have been developing in recent years in connection with irreversibility.

The physics of 'spilt water will not return to the tray' is a cutting-edge field of physics that is evolving daily toward an understanding of the ultimate mathematical structure that expresses irreversibility. Irreversibility is a profound physical phenomenon that cannot be obtained even by pursuing the motion of a single particle or the ultimate elementary particles. I hope that during your impressionable student years, you will once again recognize and be deeply moved by the existence of such physical phenomena in the natural world.