Why do systems naturally evolve towards states of higher entropy?

Systems naturally evolve towards states of higher entropy because it is statistically more probable for systems to be in disordered states.

Entropy is a measure of the disorder or randomness in a system. In the microscopic world, each state of a system corresponds to a specific arrangement of its particles. For example, if we consider a gas in a container, one state might correspond to all the gas particles being in one half of the container, while another state might correspond to the gas particles being spread evenly throughout the container. The second state is more disordered, and thus has a higher entropy.

The key to understanding why systems evolve towards states of higher entropy lies in the concept of probability. There are vastly more ways to arrange the particles in a system to achieve a disordered state than an ordered one. If we were to randomly rearrange the particles in our gas container, it's far more likely that we'd end up with a state where the particles are spread out rather than clumped together. This is because there are simply more possible arrangements that correspond to the spread-out state.

This idea is formalised in the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time. It can remain constant in ideal cases where the system is in a steady state or undergoing a reversible process. But for all spontaneous changes, the total entropy will always increase. This is often referred to as the principle of the increase of entropy.

In essence, systems naturally evolve towards states of higher entropy because these states are statistically more probable. It's a bit like if you were to throw a handful of marbles onto a chessboard - it's far more likely that the marbles would land in a disordered arrangement than in a neat row. The same principle applies to particles in a system, leading to the natural tendency for systems to evolve towards states of higher entropy.