  Quantum anomalies are the breakdowns of classical conservation laws that
occur in quantum-field theory description of a physical system. They appear in
relativistic field theories of chiral fermions and are expected to lead to
anomalous transport properties in Weyl semimetals. This includes a chiral
anomaly, which is a violation of the chiral current conservation that takes
place when a Weyl semimetal is subjected to parallel electric and magnetic
fields. A charge pumping between Weyl points of opposite chirality causes the
chiral magnetic effect that has been extensively studied with electrical
transport. On the other hand, if the thermal gradient, instead of the
electrical field, is applied along the magnetic field, then as a consequence of
the gravitational (also called the thermal chiral) anomaly an energy pumping
occurs within a pair of Weyl cones. As a result, this is expected to generate
anomalous heat current contributing to the thermal conductivity. We report an
increase of both the magneto-electric and magneto-thermal conductivities in
quasi-classical regime of the magnetic Weyl semimetal NdAlSi. Our work also
shows that the anomalous electric and heat currents, which occur due to the
chiral magnetic effect and gravitational anomalies respectively, are still
linked by a 170 years old relation called the Wiedemann-Franz law.
