To hash this out a bit, entropy is not the sum of physical laws. It isn't even a law. Entropy is a property of macroscale physics (i.e. summed over microscales in statistical physics). But there is a local law of thermodynamics (TD) that states that entropy in closed systems is maximized over time.
In this context physicists are still arguing if entropy is a property of the whole universe, a proposition that is even iffier than attributing an energy to the whole system. It seems that you can, even independently of attributing energy which latter you do from the global geometry or the system behavior. But then you have to use the holographic principle just as for black holes. And you see that it is increasing over cosmological time.
The only thing that law, the 2nd law of TD, says is that there exist irreversible systems. Its microscale statistical physics elaboration is that entropy is a measure of the energy states that are available to the system at its given energy.
Superficially the 2nd law describes disorder. But it is wrong to say that it equals an increase of disorder, since in very constrained systems the most ordered ones have the highest entropy.
Instead its use is in TD. Life is like a refrigerator, in an open system (Earth radiation to space) with an energy source (Sun) it can locally "freeze out" ordered states, as long as the energy differential is there. But the reason it can continue to do so over cosmic time is because the universe is expanding, so the entropy density is never maximized. Incidentally, nothing is "anti-enthropic", since entropy is a statistical property of all large quantum systems.
As for astrobiology here, the universe evolved complex structures early on. The oldest stars and their galaxies are more than 13 billion years old, and the oldest known planet is ~ 12.7 billion years old. Physicist Sean Carroll notes that complexity of the universe, in almost all definitions, has been increasing over cosmological time. But it has also already maximized since we are now in the exponentially expanding dark energy dominated era. Complexity will continue to dilute to zero as massenergy density does. That is apparent in your images by the way.
Earth is but 1/3 of the universe age, but it evolved life right away and complex multicellular life, starting with cyanobacteria differentiation, with the oxygenation event after ~ 2 billion years. Intelligence is, as the elephant trunk, not assured what we know, but happened ~ 2 billion years after that.
I would hence assume that the population of inhabited planets that saw complexity started to become dense ~ 11 billion years ago, and the population of inhabited planets that saw intelligence started to become dense ~ 9 billion years ago. Since we can approximate such stochastic processes with a Poisson process at first blush, its exponential increase can very well be described as a "pulse". (But a non-correlated such mind, excepting transpermia and space faring colonization.)
Given that most habitable planets will be around M stars that can live for ~ 100 billion years and a superEarth can keep its atmosphere for ~ 20 billion years, the pulse has reached roughly maximum density long since but not yet started to die out. (I'm convolving colonization into that, because it is much faster, cheaper, less risky and more rewarding to colonize Oort clouds than planets - the galactic Oort cloud is likely already filled with a stable density of silent, socially and biologically divergent, biospheres. Or it isn't and the result is unlikely to differ.) Earth will die before that.