B.4.8 (HL)—Local entropy decrease

Choose the system boundary

A non-isolated subsystem can have $$\Delta S_{\mathrm{local}}<0$$. The second law is satisfied if the surroundings increase by at least as much, so that

$$\Delta S_{\mathrm{total}}=\Delta S_{\mathrm{local}}+\Delta S_{\mathrm{surr}}\ge0$$

Examples

A refrigerator reduces the entropy of its contents but releases more entropy to the room. A growing organism becomes more ordered locally while chemical processes increase entropy in the environment.

Explain, do not just label

When a local entropy decrease is proposed, identify the energy or matter transfer across the boundary and explain where the compensating entropy increase occurs.

Common trap

“Entropy can never decrease” is incomplete. The correct statement applies to an isolated system or to the total system plus surroundings.