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Comment by Morizero | Hacker News Reader

Not true. The arrow of entropy has a direction and it's the same as the arrow of time. There's not a good explanation for why though.

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There's a perfectly good explanation for why though, in fact the explanation is what motivated the formalism of entropy to begin with. There are significantly more ways that the energy contained within a closed system can spread throughout that system than there are ways for energy contained within a closed system to condense, so that if you observe the state of a system at two different moments in time, you will expect to see it evolve towards the statistically more likely outcome than the statistically less likely outcome.

And from first principles, that's what entropy is, a measure of how energy is dispersed throughout a system. Of course once you have that first principle understanding of entropy then you can come up with more rigorous formalisms to properly quantify what it means for energy to be distributed throughout a system, such as measuring the number of microstates that correspond to a macrostate, and other various formalisms that are more or less equal to each other... but fundamentally they all start from this basic principle.

If time were running against the arrow of entropy, nobody could perceive or measure it, right? Remembering something is per se an increase in entropy, so the universe could run in negative time direction, but we would simply forget, what had happened.

That said, I personally think such thought experiments are futile and the nature of time has to be understood by its connection to causality and information.

Of course you could perceive it, measure it and record it. The entropy of your body or your brain is not necessarily increasing, nor is the entropy of your computer or other information storage systems.

Entropy only statistically tends towards an increase in closed systems and neither your computer or your brain are closed systems. They are both constantly getting energy from an external source of power and in turn dispersing previously consumed energy out into their environment.

And yet you still manage to perceive things just fine... in fact your perception of the world is unlikely to change whether or not the entropy in your brain increases or decreases by some bounded amount (of course too much of either an increase or decrease will destroy your brain).

Your claim about remembering an event, which likely alludes to Laplace's demon [1], requires an overall increase in entropy in the system as a whole, but does not require an increase in entropy in the specific part of the system that is recording the event.

Every time your computer calls a function like memset(dst, 0), or sorts a list, or arranges data into some kind of structured binary tree, your computer is decreasing its own internal entropy by taking a statistically likely arrangement of bits and transforming it into a very unlikely arrangement of bits. The decrease in the internal entropy of your computer is more than offset by an increase in global entropy but that global entropy is radiating way out into the cosmos and has no impact on your computer's ability to register information.

[1] https://en.wikipedia.org/wiki/Laplace%27s_demon

There's no arrow of entropy, it's an invented useful model to describe something that nature does. Everything is like that, I.e. there's no electric field, it's a useful way to do calculations about particle interactions.

Of course these are models. And to be able to recognise that entropy increases with time is an example for their usefulness.

Does it increase over time or does it do its thing and in our model we decided that stages of it is called time?

Right, i had the same thought. What we can say is, that the quantities we call t and S are correlated.

Absolute entropy of a system is calculated either by integrating heat capacity/temp at constant pressure from 0kelvin to the measured temperature, or by calculating via Shannon's method using average amount of information in a discrete random variable.

There is no time factor in any absolute entropy equation.

Empirically, if you measure the entropy of a closed system at a given time, and you measure the entropy of that same closed system at a different time, then calculate the deltas of each, their signs match so long as the time delta is finite and the system isn't empty. So stated plainly, as time increases, so does entropy.

By combining these first principle formulae with the empirical results on entropy, you arrive at the second law of thermodynamics. However, like I said before, we're not really sure why the signs match and it's considered to be an unsolved problem in physics.

https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p...

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