  Gravity curves spacetime. In regions where the de Broglie wavelength is very
small compared to the curvature of spacetime, the wave equations in flat
spacetime can be generalized to curved spacetime. The validity of the
formulation when the de Broglie wavelength becomes comparable to the curvature
is an open question. To test these formulations experimentally, huge energy of
the order of the Planck mass would be required. Euclideanized spacetime is used
to model thermal systems.
  In this work, an equivalence between spatial variation of temperature in
thermal baths and curvature of Euclideanized spacetime is propounded. The
variation in temperature is recast as a variation in the metric. The Dirac
equation is then solved in this curved Euclideanized spacetime. The curvature
in Euclideanized spacetime can be obtained in Chromodynamic or Electromagnetic
scale energies. If this equivalence is correct, it could provide a platform to
experimentally explore quantum mechanics in curved spacetime.
