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Time direction is determined by entropy from "summary" of A Brief History of Time by Stephen W. Hawking

Entropy, a concept from thermodynamics, can be thought of as a measure of disorder in a system. The second law of thermodynamics states that the total entropy of a closed system can never decrease over time; it can only stay the same or increase. This means that as time passes, things tend to become more disordered. In the context of the arrow of time, this increase in entropy plays a crucial role. Entropy provides a direction for time to flow in; it gives us a sense of past, present, and future. When we observe a system, we can tell the direction in which time is moving by looking at the level of entropy. For example, if we see a broken cup on the floor, we know that it must have been dropped and shattered at some point in the past. The broken cup represents a state of higher entropy compa...
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    A Brief History of Time

    Stephen W. Hawking

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