 Ergodic theory plays an important role in statistical physics, and EH, or some modification of it, constitutes an important measure of randomness in both Hamiltonian and dissipative systems. It is sometimes argued that EH is by and large irrelevant for physics because real physical systems are not ergodic. But, this charge is unwarranted, and a closer look at non-ergodic systems reveals a rather different picture, because EH can be fruitfully be used in the foundations of statistical mechanics, analyses of randomness, and chaos theory. More recently it has also played a role in understanding laws of nature (Filomeno 2019, List and Pivato 2019).