The Biggest Ideas in the Universe

Sean Carroll

3 annotations • data

First annotation on Jul 17th, 2025.

x12_Five_Time

To Laplace's Demon, who keeps track of the exact microscopic state of the world, everything would seem reversible. Then again, the Demon also knows the complete past and future. The Demon draws no distinction between "remembering the past" and "predicting the future." For the Demon, there's no real arrow of time.
It was the brilliant idea of Austrian physicist Ludwig Boltzmann in the 1870s to use this setup to suggest a way of understanding entropy. The idea of entropy had already been introduced earlier in the nineteenth century; Boltzmann's contribution was to connect this intrinsically macroscopic property to its microscopic underpinnings. Namely, he suggested that the entropy is related to the number of microstates in each macrostate.[*] From this perspective, it makes sense that entropy tends to increase over time. A low-entropy macrostate corresponds to just a small number of possible microstates, whereas a high-entropy macrostate corresponds to a large number of possible microstates. If we start in a low-entropy state and our system wanders off in some generic direction in phase space, we should expect entropy to increase simply because there are more ways (usually many, many more ways) to be high-entropy than to be low-entropy.
Entropy tends to increase because there are more ways (microstates) to be high-entropy than to be low-entropy. You may have noticed that this explanation smuggles in a hidden assumption: that the entropy started low in the first place. This idea, known simply as the past hypothesis, works together with Boltzmann's micro/macro connection to get the second law of thermodynamics off the ground.