Entropy and probability are closely connected because entropy measures how likely a particular arrangement of particles is. Here’s a way to understand it:
- Microscopic arrangements (microstates)
- Every system can exist in many possible ways at the particle level, called microstates.
- Example: In a gas, molecules can be in many different positions and speeds.
- Probability and disorder
- Some arrangements are more probable because there are more ways to achieve them.
- High probability → many microstates → high disorder → high entropy.
- Low probability → few microstates → low disorder → low entropy.
- Entropy formula (conceptually)
- Entropy increases as the number of possible arrangements (W) increases.
- More arrangements → more ways for the system to exist → higher probability → higher entropy.
Intuition:
- Nature favors probable states.
- That’s why ice melts or gas spreads: the particles move into more probable, disordered arrangements, increasing entropy.
In short: Entropy is a measure of how many ways a system can be arranged, and higher probability arrangements correspond to higher entropy.