Maxwell’s demon and the physical nature of space

Maxwell’s demon is a thought experiment to examine the second law of thermodynamics. But is not only about a special part of physics, but about some unspoken features of our Universe as well.
It is a small, intelligent entity who can detect the speed of individual molecules and opening or closing a door that divides a box into two parts, he/she is able to separate the fast molecules into one while the slow ones into the other part of the box. The result is the decrease of entropy in a closed system – that is contradicts the second law.
Or not, since, according to an argument based on information theory, the main problem is that if Maxwell’s demon’s memory isn’t infinitely large, then sooner or later information should be erased form it.This process emits heat into the box, because information erasing necessarily causes heat [Charles Seife: Decoding the Universe, p. 85.]. So the second law remains valid, since the entropy grows in the closed system.
This answer is partly based on the presupposition that only finitely large memories are possible and includes another presupposition, too, about the nature of space–after all, if you would be able to divide the space into infinitely small amounts, then it would be possible to store an infinitely large amount of information in a finite storage (at least, theoretically). I.e. If you have a two square cm surface of data storage, then you could use the first square cm to store the first piece of data; a half square cm to store the second piece of data; etc. ad infinitum.
An infinitely large memory perhaps not as unreal as it seems to be for the first sight, since there are plausible theories about hypercomputing based on relativistic spacetime of blackhole physics (see the details here). In this case manipulating an infinitely huge amount of data in an finite period of time is possible thanks to the nature: since it is presupposed that time is divisible infinitely many pieces, the result is that we have enough time to perform infinitely many operations in a finite period of time.
Ad analogiam: We can hypothesize that the space’s nature is similar and it is divisible infinitely, so it is possible to build a spatially finite storage to store an infinite amount of information. So we never should erase a bit of information–and the entropy wouldn’t rise in the box.
Obviously, nobody knows whether the space continuous, but it has been shown by this example how the laws of thermodynamics is embedded into the "environment" of the existing physical laws. And we cannot exclude the existence of Maxwell’s demon if the space we live in is not discrete, but continuous.

Where is every time traveler?

Perhaps nowhere, since they simply don’t exist, as time travel is impossible–but Einstein’s twin paradox (time dilatation, if you prefer) is nonetheless real. Notice that the time dilatation is not a proof of time travel; and that time travel and time dilatation are different questions. The first one is about whether time is similar to space in a certain sense, the second one is about what happens at very high speeds.
Obviously, time is a problematic field of modern physics. As far as we know, “the second law is the only fundamental law of physics that distinguishes between past and future” [Melanie Mitchell: A Guided Tour to the Complexity, p. 43]. Obviously, it has a kind of physical background, as the rise of entropy wouldn’t be possible without an early phase of high order (=Big Bang) but entropy’s concept is purely mathematical. I.e. in the case of the law of gravity, the gravitational force is inversely proportional to the square of distance–and this proportion cannot be deduced solely from the mathematical equations. But to understand the second law is enough to know that there are more ways to make disorder than order. What is to say, in this case there is no an additional physical law to determine the results over the logic of mathematics (opposite to gravitational law where there is a second “layer” over the mathematical description to determine that the connection between the distance and force is not, say, linear. By the way: if Newton’s law is two-layered (physics over math), then it is interesting question whether exist laws with tree, four etc. layer).
The second law creates the “time of arrow”. So since there is no any physical effect to modify its mathematics, time can be regarded as a result of the mathematics which is the basis of our time description.
British historian Arnold J. Toynbee said that history was regarded to be nothing but "one damned thing after another.” According to the logic of our argumentation, it is defendable that although time, using a kind of mathematical abstraction, can be represented as a dimension, in reality it is nothing more than “one damned thing after another”. So the meaning of travel in time is simply uninterpretable: It has no meaning at all, but it doesn’t exclude the time dilatation where according to the observers of a different frame, events follow slower each other if your speed is close to the speed of light.
Of course, it can be argued that it is a natural law that there is no an additional natural law over the level of mathematics in connection with entropy, and it can be asked why.

The origin of the multiverse

According to Aristotle our world which had a potentially infinite past and it’s spatially extension was finite, but a potentially infinite past is unacceptable today, since it necessarily ends in our present. So it is completed – and so it cannot be potential (but a potentially infinite future is still a possibility). Obviously, Aristotle’s finite space conception is similarly contradictory for us, as it is based on the belief in a finite, spherical shell of the stars that surrounds the Universe.
Newton believed in actually infinite space and finite time – namely, according to him the World was created some thousand years ago (of course, if we do not accept the existence of a final point in history, then it has a potentially infinite future).
The Big Bang Theory uses a finite spacetime model.
Last but not least, according to a common interpretation, the multiverse hypothesis presumes that both space and time is actually infinite and the Big Bang is only a bubble in the infinite sea of other bubbles. This resembles to the Steady State Theory, since it declares a spatiotemporal infinity without a beginning (and it is ironic that this obsolete model, which is forgotten in traditional cosmology, survives in this form). As far as I know, nobody examined the question of the possible origin of the multiverse as a scientific problem. Of course, if you believe that it has no origin (since it is spatiotemporally infinite), then it is a meaningless question.
But we can play either with the idea of a spatiotemporally finite multiverse that includes  only finitely many universes.The fact that we cannot able observe other worlds, does not mean that there are infinitely many of them.
Or there is a possible multiverse model where time is finite (or potentially infinite), but its space is actually infinite. In other words: it is a multiverse that was born a finite time ago but it is spatially infinite since the beginning, and it resembles to Newton’s model in a certain way. The appearance of infinity is always problematic in physics, so – at least from this point of view – this model with an instant spatially infinity is not more contradictory than the traditional multiverse interpretation with an infinite past.

Life, Universe and multiverse

According to Bernard Carr, “the Multiverse picture reduces the strong anthropic principle to an aspect of a weak one” [in Universe or Multiverse, Oxford Univ. Press, 2007, p. 4], since it explains our Universe’s biofil features by hypothesizing the existence of the multiverse. If we accept the existence of (infinitely) many other universes, it is not a surprise to find ourselves in a universe fine-tuned for life. It is a consequence of the selection effect: we can live in a universe which is suitable for life, while there many, lifeless worlds (obviously, without any intelligent observer).
This reasoning based on some unspoken assumptions.
Although Abraham Loeb argues [The Habitable Epoch of the Early Universe, 2013] that there was an opportunity for the appearance of the life already 10 – 17 million years after the Big Bang, it seems to be evident that because of the physical laws, a relative huge and old universe is needed for the appearance of life. Still in Loeb’s example, the criterions of the life didn’t appear immediately after the beginning. So at least in a world governed by our laws of physics, we have to wait for some time before the first organism can be created. Obviously, it is an interesting question whether a universe with different physical laws can produce life within the first seconds. And it is a more interesting question that how long time needed for the formation of the intelligence in another Universe. Ad absurdum, one can imagine a world where the basic elements of life are cooked in the twinkle, but evolution is another story, since it based on natural selection. So a lot of steps is needed to reach a certain complexity. The appearance of the intelligence at a very, very early period of the Universe would be a powerful argument for the existence of a Creator.
Turning back to the original questions, it seems to be a well-founded argument that there are some criterion of the emergence of life and intelligence. It isn’t possible them to come into being without some physical conditions.
It is imaginable that to the emergence of a biofil universe many other universes’ existence needed. After all, life requires a relative long past with relative huge spatial extension, and ad analogiam, it cannot be excluded that a universe fine tuned for life requires the existence of other universes.
Obviously, it seems to be a not too serious concept. But Carr’s concept is based exactly on this, since he leads back the existence of our biofil environment to the existence of other universes. According to him, our Universe was chosen by chance, but I can imagine that there is a connection between our Universe and the others, and this connection isn’t based on a kind of chance, but on some kind of physical laws.
What is more, arguing that only a few (or only one) habitable universe exists, Carr suggest that life is not a general phenomenon, but an exception. But at least theoretically it is imaginable that life is necessarily associated with the presence of the matter (although not every, but) in several universes.
Or, ad absurdum, we can play with the idea of an “Ultimate Anthropic Principle” which prohibits the born of any lifeless universe. Who knows – we have only one example for a biofil world, and it isn’t enough for generalization.