  The present thesis aimed to examine the effects of vorticity on the
thermodynamics of relativistic quantum systems. We extend the Zubarev's
non-equilibrium statistical operator method to address quantum effects induced
by vorticity in the presence of chiral matter and external electromagnetic
field and keeping full covariant and quantum properties of the system. To
investigate the effects of vorticity, this work has been focused on systems
consisting of massless chiral fermions. We recovered the significant quantum
phenomena known in the literature, namely the chiral magnetic effect, the
chiral vortical effect, the axial vortical effect and the chiral separation
effect and we also revealed the presence of additional effects at second-order
on thermal vorticity. This study has also identified and presented the exact
solutions of thermal states for a system at global thermal equilibrium
consisting of chiral massless fermions under the action of an external constant
homogeneous magnetic field. Taking advantage of these exact solutions and
conservation equations, the study also proved that the thermal coefficients
related to first-order effects on thermal vorticity do not receive corrections
from the external electromagnetic field. The same argument revealed existing
relations between those thermal coefficients, even connecting coefficients
related to vorticity to other related to electromagnetic field. For instance,
this analysis has found that the chiral vortical effect and the chiral magnetic
effect conductivities are connected one to the other by a differential
equation. Therefore, this research provides the first steps into deriving the
relations between the effects and the interplay of electromagnetic fields and
vorticity.
