Thermal Field Theory in Small Systems

We compute the finite size corrections to the partition function in a Cartesian space of finite extent in M directions and of infinite extent in D – M directions for a massless, non-interacting scalar field theory. We then use this partition function to compute numerically the energy density, pressure, entropy density, and speed of sound for this theory for M = 1, 2, and 3 for D = 3 total spatial dimensions. The finite size corrections for the speed of sound are ∼ 600%, which indicates the need to consider these corrections in hydrodynamic simulations of small collision systems in high energy nuclear physics. (paper)