Actually, this is also false. Entropy is a measure of the decrease of information when we look at things from a large scale instead of the small scale. but there are a lot of paradoxes of entropy.
For example, suppose that we have two chambers with the same gas. We open the chambers so that they mix. The entropy does not change.
If, instead, those two chambers have different gases, the entropy will increase upon mixing.
But, what happens if the gases are different, but we can't detect the difference? In that case *both* entropy calculations work. One calculation says entropy does not change and the other that it does. But both work perfectly well for that and any subsequent calculation *as long as* we cannot distinguish the difference between the gases.
So the amount of entropy depends on our state of ignorance.
But I can go even further.
If you do statistical mechanics with deterministic underlying laws, you will get the *wrong answers* in your calculations.
In fact, this was one of the first clues that the deterministic Newtonian laws were wrong: the calculations done for the heat capacity of gases got the right answers for monoatomic gases and for diatomic gases, but not for more complicated molecular gases (say, carbon dioxide).
Instead, you need to do statistical mechanics based on *quantum mechanics* to get he correct answers. So even your claim that entropy and statistical mechanics shows an underlying determinism is flatly wrong: historical facts go precisely the other way. it was statistical mechanics that gave the first clue that the deterministic description was wrong.
The term entropy was first coined in the19th century during the development of steam engines. When an energy balance was done, there was always lost energy. This measurable lost energy was coined entropy and was seem as the lost energy needed to complete the energy balance. Entropy is a measurable quantity that is still used in engineering calculations for practicals things, that need to go beyond theory. The information definition for entropy is a newer version, with lost energy explaining the loss of information integrity.
Since the 2nd law states that the entropy of the universe will increase over time, that means the universe is bleeding energy; losing energy, into ever increasing entropy. The universe is aging, due to the 2nd law with the universe losing net irretrievable energy.
We can reverse entropy, in part, and retrieve the energy due to entropy, such as by freezing water. But the overall universe is bleeding and losing net irretrievable energy or else the 2nd law is invalid. This energy is conserved; energy conservation, but not in a form that is net recyclable to the universe. This is why the universe cannot expand forever nor can it cycle back to where it came. It has a unique path based on its starting energy minus its continuous lost energy bleed, due to the 2nd law.
An interesting observation is the living state generates a lot of entropy with consciousness taking this to the limits. Essentially each of us by being alive and conscious is generating lost energy that is being conserved. The classic thinker called this realm of conserved energy, no longer connected to the material universe, the realm of the afterlife.
Entropy times temperature; TS, has the units of energy. Entropy by itself is not energy, but rather is a type of memory that structures temperature and heat. With the universe cooling from day one, the original lost energy into entropy cannot be fully retrieved, but exists as entropic information.
The quantum universe
In terms of our quantum universe, one question nobody asks is why do we have a quantum universe? What advantage does this bring to the table?
Up to the early 20th century we modeled the universe with continuous math functions. The quantum observations of the early 20th century showed that the universe was more discontinuous; quanta and gaps, with not all states possible. The net affect is our quantum universe saves time, which makes sense, since the universe is also bleeding energy into entropy. If we lived in a continuous function universe where A had to react with B, to get C, this could take forever due to infinite options that would exist between A and B. But by limiting the options; quanta, we can get to C quicker, thereby saving time. The quantum universe loads the dice of statistics.
One important paradox of scientific thinking is connected to the concept of space-time. On one hand we know we live in a quantum universe of discontinuous functions, but we still treat space-time as though it is continuous function and then add addenda like statistics. We assume space-time is continuous and when things happen that appear to defy this assumption, we assume probability.
Another way to model this is to assume that space-time has its inertial place, but space and time can also exist as separates space and separated time that can act independently of each other. If one could move in space without the constraint of time, set by space-time, we could be anywhere or everywhere in space in zero time. This classic attribute of God is called omnipresence. If we could move in time without the constraint of space we would get an information affect that synchronizes everywhere in time, such as the laws of physics being the same everywhere in the universe. This classic attribute of God was called omniscience.
If you model space-time overlapped with independently acting variables for space and time, you get a quantum universe and the affect we call probably functions. Acceleration, which are part of all forces, is one part distance and two part time; space-time plus time potential.
If we assume a dimension where space and time were independent of each other this would define a state of infinite complexity; infinite entropy, since the limits set by space-time would not apply. This state, in this model, drives our space-time universe, via the second law. It pushes us in the direction of ever increasing entropy and complexity; life and consciousness, toward itself.
This model makes it easy to form the universe, before energy or matter since these are space-time concepts that can appear from space and time not connected. Inflation is about moving space-time in space, independently of time.
