Simple one-dimensional Hamiltonian simulations

1. When the driver hits the left-hand wall, at q1=0. (Here, its velocity is drawn from the correct distribution for wall-hitting particles at equilibrium, which is ~ |v| exp(-mv^2/2). Note the factor of |v|, which is required because we are thermalizing particles when they pass a particular point. If we were thermalizing particles at particular times, this factor would be omitted.) [Similar correct thermalizations are used in situations 2 and 3 below.]
2. When the piston hits its personal wall, which we put at q2=0.001.
3. On every 200th collision between piston and driver. (This tweak was put in to avoid infinitely long simulations when the piston and driver chatter against each other.)

Demo

Energy