Does statistical mechanics imply that the universe is probabilistic?

Question

Statistical mechanics says that a system will evolve to a state of higher entropy (i.e. states with higher number of microstates) simply because it is overwhelmingly more probable than evolving to a state of lower entropy. Does this simply that the evolution of a system is inherently probabilistic?

Say we have a container of gas. According to kinetic gas theory, we can model the gas as a collection of particles that obey the law of Newtonian mechanics. But since Newtonian mechanics is deterministic (i.e. if we know the initial condition, we can know any future state with 100% certainty), the container of gas as a whole should behave deterministically. If this is the case, why do we assign probabilities to different states of a system? Is it because we don't exactly know the initial condition of a given system that we resort to probabilities?

We can't know every gas molecule initial position and velocity, because it's forbidden by quantum mechanics laws, hence at the microscopic level universe is probabilistic. At the macroscopic - deterministic, to some degree. — Agnius Vasiliauskas, May 12 '22 at 06:25
Emergence of irreversibility from deterministic laws is a somewhat complicated but well discussed subject, see, e.g., this thread. Also, that we can actually calculate the future with 100% certainty makes an assumption that we actually have the means do carry out such a calculation, see this thread for related discussion. — Roger V., May 12 '22 at 07:34
Does this answer your question? Where does the irreversiblity came from if all the fundamental interaction are reversible? — Jon Custer, May 12 '22 at 16:38
Thank you for the answers. All of the threads have been helpful. So ultimately, is it the fact that we have neither the initial conditions nor the computational power to compute the future state that forces us to use probabilistic methods? — sl2outnow, May 12 '22 at 16:43

score 2 · Answer 1 · answered May 12 '22 at 11:06

No. Statistical mechanics does not imply a non-deterministic universe.

When you ignore some information about a deterministic system you can still use probabilities. Consider a machine that flips a coin to the opposite side every 5 seconds. If we don't know how long since the machine was started, we can say there is a 50% chance of the coin being heads when we look.

Consider a machine that starts with 8x8 coins all heads, and every 5 seconds it uses a pseudorandom number generator to select a coin and flip it over. After the machine has been running for a long time we can estimate that about 50% of the coins will be heads. In principle we could calculate it using knowledge of the pseudorandom number generator and the amount of time since the machine started running. In reality we probably don't really care about calculating it like that, and we just use a probability distribution to describe the likely number of heads showing at any one time.

Does statistical mechanics imply that the universe is probabilistic?

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