  Recently, I studied the thermodynamical properties of the Einstein-Maxwell
system with a box boundary in 4-dimensions [1](JHEP 04 (2024) 083). In this
paper, I investigate those in 3-dimensions using the zero-loop saddle-point
approximation and focusing only on a simple topology sector as usual. Similar
to the 4-dimensional case, the system is thermodynamically well-behaved when
$\Lambda<0$ (due to the contribution of the "bag of gold" saddles). However,
when $\Lambda=0$, a crucial difference to the 4-dimensional case appears, i.e.
the 3-dimensional system turns out to be thermodynamically unstable, while the
4-dimensional one is thermodynamically stable. This may offer two options for
how we think about the thermodynamics of 3-dimensional gravity with
$\Lambda=0$. One is that the zero-loop approximation or restricting the simple
topology sector is not sufficient for 3-dimensions with $\Lambda=0$. The other
is that 3-dimensional gravity is really thermodynamically unstable when
$\Lambda=0$.
