Can entropy ever decrease in a closed system?

No, according to the Second Law of Thermodynamics, the total entropy of an isolated system (one that cannot exchange energy or matter with its surroundings) can never decrease over time. It can only stay the same or increase.

It is important to clarify the terminology:

• Isolated System: No energy or matter exchange. Total entropy must increase or stay the same.
• Closed System: Can exchange energy (like heat) but not matter.

In a closed system, the entropy *can* decrease, but only if it exports a larger amount of entropy to its surroundings. For example, a refrigerator (a closed system) cools its contents, decreasing their internal entropy. However, it does this by running a compressor and releasing a large amount of high-entropy heat out the back. The total entropy (refrigerator + kitchen) increases.

The only exception to this rule is on a microscopic level. Statistical mechanics, which defines entropy as a measure of probability, allows for tiny, random, and temporary fluctuations where a small number of particles might briefly arrange themselves into a more ordered (lower entropy) state. However, the probability of this happening for any significant number of particles or for any significant duration is astronomically small, making it a statistical impossibility on the macroworld scale.