Until the End of Time: Mind, Matter, and Our Search for Meaning in an Evolving Universe

by Brian Greene

we have now illustrated the essential concept of entropy. The entropy of a given configuration of the pennies is the size of its group—the number of fellow configurations that pretty much look like the given configuration.9 If there are many such look-alikes, the given configuration has high entropy. If there are few such look-alikes, the given configuration has low entropy. All else being equal, a random shake is more likely to belong to a group with higher entropy since such groups have more members. This formulation also connects with the colloquial uses of entropy I referenced at the outset of this section. Intuitively, messy configurations (think of a chaotic desktop piled high with scattered documents, pens, and paper clips) have high entropy because a great many rearrangements of the constituents all pretty much look the same; randomly rearrange a messy configuration and it still looks messy. Orderly configurations (think of a pristine desktop with all documents, pens, and paper clips neatly placed in their designated positions) have low entropy because very few rearrangements of the constituents look the same. As with the pennies, high entropy beckons because messy arrangements far outnumber orderly ones.