  The Unruh effect has been investigated from the point of view of the quantum
statistical Zubarev density operator in space with the Minkowski metric.
Quantum corrections of the fourth order in acceleration to the energy-momentum
tensor of real and complex scalar fields, and Dirac field are calculated. Both
massless and massive fields are considered. The method for regularization of
discovered infrared divergences for scalar fields is proposed. The calculated
corrections make it possible to substantiate the Unruh effect from the point of
view of the statistical approach, and to explicitly show its universality for
various quantum field theories of massless and massive fields. The obtained
results exactly coincide with the ones obtained earlier by calculation of the
vacuum average of energy-momentum tensor in a space with a conical singularity.
Thus, the duality of two methods for describing an accelerated medium is
substantiated. One may also speak about the emergence of geometry with conical
singularity from thermodynamics. In particular, the polynomiality of the
energy-momentum tensor and the absence of higher-order corrections in
acceleration can be explicitly demonstrated.
