Detailed balance

Detailed balance is like following the rules of a game. Imagine you are playing a game where you have to follow certain rules to win. For example, in chess, you have to move your pieces in a certain way to capture your opponent's pieces and protect your own. If you don't follow the rules, you will lose the game.

In the same way, detailed balance is like following the rules of a game in physics. It applies to systems that are in thermal equilibrium, which means they are at a constant temperature and all the particles in the system are not moving or changing anymore. Detailed balance requires that the rate of any process that can occur between two states must be exactly the same as the rate of the reverse process going back to the original state.

Imagine you have a bathtub with water that's at a certain temperature. If you want to add hot water to the tub, the hot water will mix with the cold water until the temperature of the bathtub water matches the temperature of the hot water. If you keep adding hot water faster than the water in the bathtub can cool down, the temperature will keep going up until it's too hot. Detailed balance requires that the rate of adding hot water is equal to the rate of the water cooling down to match the temperature.

In physics, detailed balance is important because it helps us understand the behavior of particles in a system. If we know the rates of the forward and reverse processes, we can predict how much energy is exchanged between the particles and how they will behave over time. It's like knowing the rules of a game so you can strategize and make the right moves to win.