I have read COUNTLESS explanations, countless examples, countless ELI5s. But I still have no fucking idea what entropy is. I’m **not** leaving this earth before I understand what it is. Thank you.
In: Physics
You can see the entropy of a system as the amount of information you gain by looking at the system (measured in bits).
Let’s examine the entropy of a single switch. If you know that this switch is stuck in the ON position, you will gain zero information from looking at it. So the entropy is 0.
If now the switch can be both ON and OFF, its entropy is not 0 because you cannot know with certainty its position before looking at it. So what is its value? Well it depends. Imagine you know that 2/3 of the times it’s in the ON position. Then you have a better chance at guessing its position as if it was 50-50. Thus, you gain less information by looking at the switch if chances are 2/3-1/3 or 1/3-2/3 than if they are 50-50 (1/2-1/2). So the entropy of the switch is maximal when the odds are even, ie when it can be in each state with equal probability.
Now consider a system of 100 switches. It can be in 2x2x2x… 100 times states, or 2^100. The number of states is immensely more, but the same rule holds: entropy is maximal when the odds are equal between all states. Or course this maximal is a lot higher than for a single switch because you need to take information on 100 switches (actually it’s simply 100x as much). The universe is the same, just with a lot more degrees of freedom.
You perhaps know the second law of thermodynamics: entropy always increases. This means that any physical system tends towards equalizing the odds. Physically, equal odds correspond to homogeneous systems. That’s why ink irreversibly diffuses in water: it’s pushed by entropy.
About heat: heat makes particles more agitated. They move around more. Let’s say particle A can be in position 1, 2 and 3. When it’s cold it’s gonna be in position 2 90% of the time and in position 1 and 3 5% of the time each. When it’s hot it’s gonna be 40% of the time in 2 and 30% of the time each in 1 and 3. So heat pushes towards equal odds. A consequence is that the second law makes heat easy to create but hard to destroy. You can convert electrical or mechanical energy to heat with almost perfect efficiency, but the opposite direction is much less efficient (typically 30-50%).
Final point: making a cold object 10° warmer increases entropy more than making a hot object (of the same mass) 10° warmer. In terms of entropy creation, there are diminishing returns with temperature. That’s why if you put a hot and a cold object in contact, physics will dictate that the heat flows from the hot object to the cold one until they reach equilibrium. Cooling down the hot object destroys less entropy than is created by warming up the cold one.
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