Quantum entanglement might be responsible for arrow of time in subsystems through decoherence. However, the arrow of time for the wavefunction of the universe seems like a different question.

Before looking for the wave-function of the universe, try to write a wave-function for yourself, and see if it can be done.

What is your weight? Shall we say 70Kg? With which velocity you walk on the street? Shal we say you go slowly, at 1m/s? Then your wavelength is

λ = h/(mv) = 2π×10-27/(7×104×100)cm ≈ 10-33cm.

Now, what are the linear dimensions of your body? Shall we say that you are rather slim and you have a waist of 30cm? Compare that with your wavelength.

In order to become a quatum object, which has a wave-function, your wavelength has to be a good couple of orders of magnitude bigger that your linear dimensions, and not vice-versa.

So, do you still want to find a wave-function for the Universe?

It doesn't. Quantum entanglement doesn't have anything to do with any such asymmetry. It simply describes the fact that probability distributions don't factorize in non-relativistic quantum mechanics. Since they don't factorize, integrating out degrees of freedom leads to a non-local description for the degrees of freedom that haven't been integrated out. 

I attached the paper on which the link Alimjan Abla gave is based. I usually do not pay much attention to popular accounts in the news that say things like "New Quantum Theory Could Explain the Flow of Time", if you believe those cancer should have been cured ages ago.

This certainly is an interesting paper, and deserves study, but even if the basic idea is correct there is a lot of work to be done. There are several important aspects missing. The first is the complete lack of any time scale for the equilibration process.  We know that a hot cup of coffee reaches room temperature in a matter of hours, and not the life time of the universe. Secondly, it is not clear if a subsystem will evolve to equilibrium regardless of the initial conditions, whatever "equilibrium" is.  Shouldn't the time scale emerge from the process envisioned (I don't think there is an intrinsic time scale in entanglement)? Actually I do not even see how they show that the state is in thermal equilibrium the way we usually understand that. They state:  "Indeed, since the bath is completely arbitrary, so is the equilibrium state of the system. In other words, the equilibration phenomenon that we describe is a general phenomenon and need not have any “thermal” aspects at all."  Although they mention earlier that under certain additional conditions the equilibrium state can be written as a Boltzmann distribution, this is not worked out or proven in the paper, and they do not show that a thermal bath leads to a thermal subsystem. Or even what the subsystem looks like for a given bath distribution function.

However flawed some of the 19th and 20th century ideas may be, the methods that were developed gave the possibility to also derive known dynamical laws describing equilibration, (e.g. laws of Fourier, Fick, Navier Stokes) and give expressions for the coefficients occurring in them (take the Boltzmann equation as an example). The ideas of the paper give no indication on how to proceed doing something like that.

So, for the moment I would not ask "How does quantum entanglement drive the arrow of time?", but just "Does quantum entanglement drive the arrow of time?", and I don't think it does. But don't take my opinion as important, there is a lot (and I mean a lot) of recent literature about it, and no general agreement at all on almost any of the aspects.

What's, apparently,  missing in their analysis is the distinction between thermal fluctuations and quantum fluctuations. What they seem to showi is that a quantum system is in equilibrium with its quantum fluctuations and that subsystems of such a systems are in equilibrium with each other in that sense. But one would have thought that to be known... The quantum fluctuations are controlled by Planck's constant-thermal fluctuations would be controlled by a temperature, however, that's a distinct parameter.  And equilibrium with respect to the former is distinct from equilibrium with respect to the latter.

Hello and hope you are doing well.

For new advances about quantum entanglement , photon and time , please refer to these links.Then we discuss more.All opinions and ideas will be acknowledged. 

https://www.quantamagazine.org/20160119-time-entanglement/

https://www.quantamagazine.org/20140416-times-arrow-traced-to-quantum-source/

https://www.edge.org/response-detail/26790

Eric M Howard

Sir,

I would like to know that good books/works on this field, I am a true beginner in this field.

thankyou

This is a good article on it : Article Time, the Arrow of Time, and Quantum Mechanics