1.2 Probability, Thermal Equilibrium, and Entropy

Microstates and Macrostates

A microstate is one specific arrangement of a system's particles, while a macrostate is the overall condition described by measurable properties like temperature and pressure. Many microstates can correspond to the same macrostate. Systems naturally evolve toward macrostates with the greatest number of possible microstates, since these are statistically most probable.

Entropy and Probability

Entropy measures the number of microstates available to a system — more microstates means higher entropy. Isolated systems tend toward states of maximum entropy because these are overwhelmingly more probable than ordered, low-entropy states. This statistical tendency underlies the second law of thermodynamics: entropy of an isolated system tends to increase over time.

Thermal Equilibrium

When two objects at different temperatures interact, energy flows from hotter to cooler until they reach thermal equilibrium, where both have the same temperature. This occurs because the combined system's total number of microstates — and thus its entropy — is maximized when energy is spread evenly, making equilibrium the most probable final state.

Key terms

Microstate

One specific, detailed arrangement of a system's particles.

Macrostate

The overall observable condition of a system (e.g., temperature, pressure), consistent with many possible microstates.

Entropy

A measure of the number of microstates available to a system; higher entropy means more possible microstates.

Second law of thermodynamics

Isolated systems tend to evolve toward the macrostate with the greatest number of microstates, so total entropy tends to increase.

Thermal equilibrium

The state reached when two objects reach the same temperature and net energy transfer between them stops, maximizing total entropy.

Try an AP-style question

Why does heat flow spontaneously from a hot object to a cold one?

1. Hot objects always contain more mass
2. Spread-out energy has far more microstates
3. Cold objects naturally attract heat energy
4. Heat always flows toward higher temperature