If you let processes that can go both forwards and backwards sit long enough, they will reach “dynamic equilibrium.” This sounds like an oxymoron because things at equilibrium are constant, right? Well, molecules are always spontaneously bumping into each other and exchanging energy. What we perceive as stuff moving in one direction just means that the rate of stuff in that direction is greater than the rate of stuff in the opposite direction. If the rate of stuff going forward is equal to the rate of stuff going back, there will appear to be no net rate of change (equilibrium) in the system but clearly stuff is still being exchanged (dynamic).

For example, let’s say we have two cups half full (half empty works, too) of water but one cup is at 60O and the other cup is at 40 O. If we put them next to each other and let them sit, eventually all the water will be 50 O (ignoring any other affects). At first the fastest rate of change of temperature for the system will be the first moment they are touching as that will be the greatest difference in temperature. After that moment, the water in the cold cup will be a little warmer than 40O and the water in the warm cup will be a little colder than 60O and the rate of heat transferred will slow down. Both cups will be closer to their equilibrium temperature. Similarly to how more snow melts on a warm day than a cold day, 60O water will transfer heat faster to 40O water than 55O water will transfer heat to 45O water. This process will continue more and more slowly until the system reaches its equilibrium temperature. The further a system is from equilibrium, the faster it will want to race to equilibrium. Because the rate of change of the forward process equals the rate of change of the backward process at equilibrium, you can express the temperature as an asymptote that never quite gets to the final equilibrium temperature. You can express the final temperature as the limit when time approaches infinity or when the net rate of change of the stuff you are talking about is equal to 0. (derivative = 0)

This does not only hold true for temperature, but also for concentrations, momentum, energy, forces and countless other quantities that can be transferred within a system. Systems at equilibrium generally offer situations with lower energy states than what the system was in before; similar to the idea of taking the path of least resistance. Although the concept lends itself to chemistry and physics, it can also be applied broadly to topics like behavior analysis, economics, populations, and many other seemingly unrelated disciplines. Even your body is doing everything it can to stay at homeostasis, its equilibrium.