box closed off at one end by a piston, and imagine that we act on the gas by pulling the piston outward. In the context of Eq.\[eq:nwt0\], this system has recently been studied by several groups [@LuaGrosberg05; @Sung05; @Lua05; @Bena05]. Of particular relevance to the present paper is the analysis of Lua and Grosberg [@LuaGrosberg05], who showed by explicit calculation that, in the fast piston limit, the dominant realizations are characterized by particles with initial velocities sampled from deep within the tail of a Maxwellian distribution; and for the reverse process, when the piston is pushed into the gas, the dominant realizations are those for which there are no particle-piston collisions [@Lua05]. These conclusions are consistent with the discussion below.

Let $n_p \gg 1$ be the total number of particles, each of mass $m$. Imagine that we begin with the piston at a location $A$, corresponding to a box of length $L$, and we prepare the gas in canonical equilibrium at temperature $T$, i.e. with particle velocities sampled independently from a Maxwellian distribution. Now we rapidly pull the piston outward, from $A$ to $B$, over a time $\tau$ and at constant speed $u=L/\tau$, thus increasing the length of the box 