Equilibrium for very small amounts of reactants Is there any difference in the concept of equilibrium when it comes down to dealing with extremely small amounts of reactants?

Say we have $$\ce{A + B &lt;=&gt; C + D}$$
 and $K_c$ is $100,000$. If we only have $10$ atoms of each $\ce{A}$ and $\ce{B}$ in a beaker, we would expect the container to be totally full of $\ce{C}$ and $\ce{D}$. But $K_c$ is not infinite, so there must be some unreacted $\ce{A}$ and $\ce{B}$. However, if there was even one atom of reactants, the reaction would quickly shift back to satisfy the equilibrium.

Does the concept of equilibrium only apply to macro-sized reactions? Is there an extendable concept for the micro scale?
Thermodynamics is only applicable to the systems of size in between astronomic and microscopic scales. Systems with a small number of particles can spontaneously abandon
equilibrium state due to fluctuations. Statistical physics tells us [1] that the relative magnitude of the fluctuations of thermodynamic quantities $x$ (e.g. pressure, temperature, volume, internal energy, entropy etc.) is inversely proportional to the root of the number of particles in the system:

$$
\frac{
\sqrt{\left\langle\left(\Delta x \right)^2\right\rangle}
}{
\left\langle x \right\rangle
}
\sim
\frac{1}{\sqrt{N}}
$$

Lets arbitrarily set the detection limit for experimental determination of the relative change of $x$ to optimistic value of $10^{-8}$. In this case we would need at least $N = (10^{-8})^{-2} = 10^{16}$ particles belonging to the thermodynamic system before we can speak of equilibrium at all. 

References


Landau, L. D.; Lifshitz, E. M. Statistical Physics, 3rd Edition, Part 1: Vol. 5; Butterworth-Heinemann: Amsterdam u.a, 1980.