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

by Brian Greene

To summarize: Having fewer molecules, or having lower temperature, or filling a smaller volume results in lower entropy. Having more molecules, or having higher temperature, or filling a larger volume results in higher entropy. From this brief survey, let me underscore one way of thinking about entropy, lacking in precision but providing a useful rule of thumb. You should expect to encounter high-entropy states. Because such states can be realized by a great many different arrangements of the constituent particles, they’re typical, pedestrian, easily configured, a dime a dozen. By contrast, if you encounter a low-entropy state it should command your attention. Low entropy means there are far fewer ways the given macrostate can be realized by its microscopic ingredients, and so such configurations are hard to come by, they’re unusual, they’re carefully arranged, they’re rare. Step out of a long hot shower and find the steam uniformly spread throughout your bathroom: high entropy and totally unsurprising. Step out of a long hot shower and find the steam all clustered in a perfect little cube hovering in front of the mirror: low entropy and extraordinarily unusual. So unusual, in fact, that were you to encounter such a configuration you should be extremely skeptical of the explanation that you’ve simply come upon one of those unlikely things that on occasion happen. That could be the explanation. But I’d bet my life it isn’t. Just as you’d suspect there’s a reason beyond mere...