Entropy changes depend on what is included inside the system boundary. In AP Physics 2, the crucial idea is that isolated systems cannot show a net entropy decrease, while closed systems sometimes can.

Why the system boundary matters

Whether entropy can decrease depends on how the system is defined.

This diagram compares open, closed, and isolated thermodynamic systems by showing what can cross the system boundary. The key distinction for entropy reasoning is that an isolated system exchanges neither matter nor energy with its surroundings, whereas a closed system can exchange energy but not matter. Seeing the boundary and transfer arrows makes it easier to decide which entropy constraints apply to the chosen system. Source

If the boundary includes everything involved, no energy enters or leaves, and the entropy rule is very strict. If the boundary includes only one part of a larger situation, energy may cross that boundary, so the entropy of that chosen part may either increase or decrease.

When discussing entropy, it is important to distinguish the chosen system from the surroundings, which are everything outside the boundary.

This figure illustrates a thermodynamic system separated from its surroundings by a boundary (here, the gas in a cylinder beneath a piston). It reinforces that “surroundings” means everything outside the chosen boundary, so energy crossing the boundary changes the system’s entropy while also affecting the surroundings. This boundary-based view is exactly what underlies the additivity idea $\Delta S_{total}=\Delta S_{system}+\Delta S_{surroundings}$. Source

A change in entropy is written as $\Delta S$. A positive $\Delta S$ means entropy increases, while a negative $\Delta S$ means entropy decreases.

Isolated systems

An isolated system is the most restrictive case for entropy analysis.

Because no energy enters or leaves an isolated system, any change must happen entirely through internal rearrangements. One part of the isolated system cannot become more ordered unless another part changes in a way that prevents the total entropy from dropping below its starting value.

For an isolated system, the total entropy change satisfies $\Delta S_{isolated}\ge 0$. In words, the entropy of the whole isolated system can stay the same or increase, but it cannot decrease. A zero change is the limiting case in which the process adds no extra entropy.

This idea is especially important because students sometimes notice that one region becomes more ordered and incorrectly conclude that entropy has decreased overall. In an isolated system, that local decrease must be balanced by an equal or larger increase somewhere else inside the same system.

A useful bookkeeping relationship is shown below.

If the chosen system is actually the entire isolated setup, then there is no external surroundings to exchange energy with, so the total entropy of that isolated setup cannot become negative.

Closed systems

A closed system is less restrictive than an isolated system.

Because energy can cross the boundary of a closed system, the entropy of that system alone can decrease. Energy transfer in either direction means the system is not constrained in the same way as an isolated system. The sign of $\Delta S_{system}$ depends on the particular interaction with the surroundings.

This does not mean entropy has been destroyed. Instead, energy transfer causes entropy changes in both the system and the surroundings. If the system transfers energy to the surroundings, the system may become less thermally disordered and its entropy may decrease. If the surroundings transfer energy to the system, the system’s entropy may increase. The important comparison is not just the sign of $\Delta S_{system}$, but the combined change for the larger situation.

So, for a closed system:

• $\Delta S_{system}$ can be positive

• $\Delta S_{system}$ can be zero

• $\Delta S_{system}$ can be negative

A negative entropy change for the system is allowed as long as the entropy change of the surroundings makes the overall entropy change of the larger isolated combination nonnegative.

Comparing isolated and closed systems

The most common AP confusion is mixing up the entropy of a part with the entropy of the whole.

• For an isolated system, there is no energy transfer across the boundary, so the entropy of the whole system never decreases.

• For a closed system, energy transfer across the boundary is possible, so the entropy of the chosen system may decrease.

• A decrease in the entropy of a closed system does not violate physics if the surroundings undergo an equal or greater entropy increase.

• Entropy restrictions apply most strongly to the total isolated combination of system plus surroundings.

This is why wording matters. A prompt may ask about a metal block, a gas sample, or a liquid, while the surroundings are not part of the named system. In that case, a decrease in the system’s entropy may be completely acceptable.

How to reason through problems

When analyzing entropy changes, start by identifying the boundary.

• Ask whether the problem’s system can exchange energy with its surroundings.

• If the answer is no, treat it as isolated and require $\Delta S\ge 0$ for the whole system.

• If the answer is yes, treat it as closed and allow the system’s entropy to increase or decrease.

• Then decide whether the question is asking about the system only or about the system plus surroundings.

Another useful habit is to watch for phrases such as insulated, sealed, in contact with a reservoir, or surrounded by air. These phrases help determine whether energy transfer is possible and whether entropy may decrease for the selected system.

Do not assume that “more order” automatically means the entropy of the relevant whole system has decreased. In closed-system problems, order may increase inside the system only because energy transfer causes a greater entropy increase outside it. The entropy rule must always be applied to the correct boundary.