Science · Information

What Is Entropy?

Why disorder wins, why information can be measured, and why time has a direction.

The question

Why does milk mix into coffee but never unmix?

The short answer

Entropy counts how many ways a system can be arranged without looking different. Disordered states vastly outnumber ordered ones, so systems drift towards them, and that drift gives time its direction.

Sorted: very few arrangements Mixed: astronomically many
Start with two separated colours and shuffle at random. Mixed arrangements vastly outnumber sorted ones, so mixing is what you see.

What science knows

Established Science

Rudolf Clausius coined “entropy” in 1865. The second law of thermodynamics says the entropy of an isolated system tends not to decrease.

Ludwig Boltzmann explained why: S = k log W, where W is the number of microscopic arrangements consistent with what we observe. The formula is engraved on his tombstone in Vienna.

The pattern

Established Mathematics

In 1948 Claude Shannon defined information entropy, the average surprise of a message, in bits. A fair coin flip carries 1 bit; a fair six-sided die about 2.58 bits (log₂ 6).

What is still uncertain

Active Research

Why the universe began in such a low-entropy state, which is what lets entropy keep rising, is an open question in cosmology, sometimes called the “past hypothesis”.

Why humans find it interesting

Cultural Tradition

Entropy has become a metaphor for decay and disorder in literature and everyday speech, often more loosely than physicists use it.

CUE perspective

CUE Perspective

Entropy is a reminder that order takes energy to keep, whether in a room, a schedule or a relationship.

CUE borrows no physics from it; the metaphor is simply useful: small, regular attention holds things together better than rare effort.

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Sources

  • Clausius, “Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie”, Annalen der Physik 201 (1865)
  • Shannon, “A mathematical theory of communication”, Bell System Technical Journal 27 (1948)
  • Carroll, From Eternity to Here: The Quest for the Ultimate Theory of Time (Dutton, 2010)

Written by CUE from the sources above. Some topics were suggested by Polymath; its claims are not reproduced.