Why does entropy increase over time?

In this video I use an example of two mixing gases to explain why entropy increases over time. Entropy is a measure of disorder, and so it is zero when gases are nicely separated and then starts to increase when the gases start to mix. A situation of order – gases nicely sorted into their own chambers – is less probable than a situation of disorder – in which gases are mixed. And so, as the system evolves, a situation in which entropy is higher is more likely than a situation in which entropy is lower. This is why entropy has to increase. Entropy can also decrease, if accidentally the gas gets unmixed. But because order is less likely than disorder, a decrease in entropy is less likely than its increase.

To sum up, entropy is defined as a measure of disorder, which is often high and rarely low. And so, by definition, entropy is likely to increase and unlikely to decrease. There is no deep physics here. Just clever definitions.