Originally Posted by
Garnier Fructis
The order interpretation of entropy doesn't come from the heat concept, but from statistical mechanics, where entropy is thought of as (roughly) the logarithm of the 'number of states' (i.e. configurations) which achieve that. Hence, the more ways you can achieve something, the higher the entropy. That's why Boltzmann attached the idea of disorder to it. Because there are less ways for the system to spell out "Thug Life" than for the system to just be a uniform soup, so for him "Thug Life" is much more ordered than equilibrium.
That being said, order and disorder are probably bad ways to describe entropy. If you have a deck or cards arranged by number and suit and you randomly switch 3 cards, did the system gain entropy? Well, the second configuration is certainly 'less ordered', but the entropy did not change because all that happened was one configuration was changed to another equally likely configuration.