  We propose a method to extend the fast on-the-fly weight determination scheme
for simulated tempering to two-dimensional space including not only temperature
but also pressure. During the simulated tempering simulation, weight parameters
for temperature-update and pressure-update are self-updated independently
according to the trapezoidal rule. In order to test the effectiveness of the
algorithm, we applied our proposed method to a peptide, chignolin, in explicit
water. After setting all weight parameters to zero, the weight parameters were
quickly determined during the simulation. The simulation realised a uniform
random walk in the entire temperature-pressure space.
