Time’s Almost Reversible Arrow

Then it is the universe expansion that made the entropy per volume decrease, actually allowing complex systems to evolve. The expansion still has to occur faster than the entropy increase rate but I read somewhere that the universe total entropy did not increase that much since the Big Bang.

This one thing I don't understand about the 2nd law of thermodynamics: given enough time won't the system go back to a more organized state simply by chance? And in that case, wouldn't the total entropy be reduced?

However, the argument can apparently be extended to the conclusion that, in a probabilistic sense, your consciousness is just a sliver of a random fluctuation of a near-maximal entropy state. Feynman argued[2] that this shows we do not arise from a random fluctuation, because (even though we're conscious), when we look far away the universe looks highly organized.

Note that those arguments make a bunch of assumptions that may not be valid in our universe, and may not make cosmological sense (entropy is not well defined cosmologically).

[1] https://en.wikipedia.org/wiki/Boltzmann_brain

[2] http://blogs.discovermagazine.com/cosmicvariance/2008/12/29/...

taken as a closed system, our Universe's initial state was a heat-death and it would stay here, nothing would happen. Fortunately or unfortunately our Universe is embedded into previous very old and cool Universe, and this gradient is what drives the expansion of our Universe and thus provides for all the things we see happening to happen, including life (which is just entropy maximizing process in some conditions).

100-200+B year later our Universe will too be very cool and expanded very "thin". The matter will be collected into several hyper-super-black holes with Schwarzschild radii of tens or even hundreds o billions of light years - some probably bigger than our visible Universe (which has 10B light years Schwartzild radius). The matter inside a regular black hole is neutrons being driven into higher and higher states as result of mass being added into the black hole. At some point the neutrons get to split into gluons/quarks and those would continue to be driven into more energetic states as more mass is added, and may be split as a result into something else too. At the same time the space around becomes "thinner" and cooler. At some point, when even more mass is added, and thus this "soup" becomes even more energetic, beyond currently known physics unfortunately, something happens to the gravitational force what has been keeping it together and it explodes and start expanding (as there is extremely high gradient between the "soup" and the space of the old Universe - thus that will be a birth of new Universe inside our old Universe, inside the parent Universe of our Universe ... ad infinitum ... with non-zero gradient, though smaller and smaller as parent-child Universe pair is getting older...

Entropy does not always increase in time, because entropy is rarely a function of time. The most common meaning of the word is a thermodynamic quantity that is not, in general, defined in non-equilibrium states. It is a function of state variables rather than time.

What people are talking about when they say "entropy increases in time" is actually some variant of minus Boltzmann H-function. This kind of resembles thermodynamic entropy, but is a distinct and less general concept. There are processes where entropy gets higher but "entropy" (minus Boltzmann H-function) get lower.

If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. It is not even clear how to define entropy of the system in between, since it is in highly non-equilibrium state.

Perhaps in zero-g, under the effect of no acceleration and/or gravity. But I've seen all (most of) the non-water bits settle in the bottom of a bottle left alone for a long time.

That doesn't detract from your overall point about entropy, but it's probably to use an example based on the quality of energy (try to generate electricity from the heat that leeches from the walls of your cabin in winter).

Here's a possibility: if you "start" at a random state, after enough exploration of the state space, there would be a local minima that was arbitrarily well-ordered. Both directions of time would then view that as the "past", and the other direction as "future".

These perceptions as to the arrow of time would last until a state equivalent to heat death is reached, at which point the "arrow" of time would flip around again.

Consider what it would look like if you ran the solar system in reverse - all the planets and moons would go backwards in their orbits, but gravity still works exactly the same. The equations of mechanics don't care about time.

And yes, information being lost in black holes would be an issue, if true - that's why that problem has been studied so much recently.

If you go to the 'overview' section, there is a nice snippet explaining all this. It points out that gravity works fine in a universe that is running backwards, however entropy is decreasing instead of increasing.

How would the reversing process know the direction and momentum to reverse for each particle?

The Copenhagen (traditional) interpenetration of quantum mechanics posits that when a system gets large enough [0] these superimposed states collapse down to a single state. This interpenetration does pose a problem with time reversibility, as if you run time backwards, then forwards again, it is not guaranteed that you will arrive in the same state after collapse.

A more modern interpenetration is Many Worlds. In this interpenetration, there is no collapse. So when we observe the cat, the universe is in a superposition of us having observed a dead cat, and us having observed a living cat. When we run time backwards, we end up at the point where we put the cat into the box, as you would expect. If we run time forwards again, we arrive at the same superposition of observing a living cat, and observing a dead cat.

Without looking at the math, the ability to go from a superimposed state to a pure state may seem like it presents an asymmetry, but the equations allow (and we have experimentally done) this in forward time already. As it turns out, the mechanism that allows for this to happen (interference) is the essence of quantum computation.

[0] The standard phrasing is is "gets measured". I read this as "gets large enough" because we could, in principle, consider the measurement device to be part of the system.