  Fluctuation theorems establish connections between fluctuations and
irreversibility by considering stochastic thermodynamic quantities. In this
study, we derive special relativistic covariant fluctuation theorems by
defining covariant work, heat, and entropy. We focus on a driven scalar field
in contact with a Markovian heat bath. For moving inertial observers relative
to the heat bath, both the energy components and the momentum components of
work and heat must be included to formulate the corresponding fluctuation
theorems, and the four-velocity of the heat bath plays an important role. It
turns out that, the irreversibility is characterized by the conventional
thermodynamic quantities in the rest reference frame of the heat bath,
regardless of the reference frame of the observer. Even in the nonrelativistic
case, the above identification is nontrivial. We study the work statistics for
a Klein-Gordon field in a driving process measured by a moving inertial
observer to explicitly verify the covariant version of the Jarzynski equality.
