Time's arrow points in the direction of increasing entropy from "summary" of The Fabric of the Cosmos by Brian Greene
The concept of time's arrow pointing in the direction of increasing entropy is a fundamental aspect of the way we experience the passage of time. Entropy, a measure of disorder or randomness in a system, plays a crucial role in understanding why time seems to move in a particular direction. In our everyday experience, we observe that things tend to move from states of order to states of disorder. For example, a cup of hot coffee left on a table will eventually cool down and reach room temperature, becoming more disordered in the process. This is due to the second law of thermodynamics, which states that in a closed system, entropy will tend to increase over time. When we look at the universe as a whole, we see that the overall trend is towards increasing entropy. Stars burn out, galaxies drift apart, and energy is dispersed throughout the cosmos. This relentless march towards disorder is what gives time its directionality. But why does entropy tend to increase over time? One way to think about it is in terms of probabilities. In a highly ordered state, there are fewer ways for the particles in a system to be arranged. As the system evolves, it is more likely to move towards states with higher entropy, simply because there are more ways for the particles to be arranged in a disordered state. This asymmetry in the way systems evolve over time is what gives us the sense of an arrow of time. We remember the past but not the future, we see things decay but not un-decay, and we know that we can't turn back the clock and restore order to a system. All of these observations are rooted in the fact that time's arrow points towards increasing entropy.
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