So to be a bit careful about how we go about defining things. Yes entropy will still be directly tied to an ensemble in that it is directly related to the probability of an observation. Probability of course being tied to thousands of observations. But the key is that entropy can be observed in any type of probabilistic system and will very often behave the same way in a system with millions of atoms or a system of a single particle. It will just be tied to different averages such as the time average, spacial average, etc.

Where entropy is distinguished between many other bulk properties is that the later are often the result of thousands of atoms acting in unison where as entropy can be observed even in a single particle system. It's especially true when talking about quantum descriptions of molecules.

For a single particle the Jacobian of the principle coordinate is the entropy term.

Say for example you have a classical particle who is attracted to a single point by the equation

E(r) = 1/2 * k * (r-r0)^2

In this system we can simply write the Jacobian as a function of r. For an N-dimensional system

J(r) = r^(N-1)

Assuming we integrate the angular terms out. If you perform a simulation of the particle with a given momentum. One of the things of course in a system with conserved momentum is that while the lowest energy position is a distance from the center r0, the time average position will only be r0 if we perform the simulation in 1 dimension. If we have two dimensions you will notice the value will be some value above r0. And as we add more and more dimensions the particle will deviate more and more from r0 outwards. That is because as you increase the number of accessible dimensions you increase the translational entropy. A hyper-dimensional particle will spend very little time near r0 despite r0 being the most stable position.

You don't need multiple equivalent systems to observe this. The time average of a single particle will give rise to this.

In statistical mechanics and such we usually define these in terms of a number of equivalent systems because in practice that's what we are typically measuring and we take advantage of the ergodic hypothesis to link the time average to other averages of interest. But the thing about entropic effects is that they show up even in atomic and sub-atomic systems and many behaviors are a direct result of it. For example if an electron can be excited to a higher set of orbitals where all the orbital is the same energy and one orbital has more momentum numbers than another sub-orbital that orbital will be preferred simply because there's more combinations that suborbital has.

Larger systems have more degrees of entropy they can take advantage of such as swap entropy, rotational entropy, etc. but the rules and interpretations are still very much the same no matter if you got 1 million particules or just one. That's not always the case for other bulk properties. Sometimes the bulk properties are only observable in the limit of the average and not on a single particle.