Detecting Majorana fermions in experimental realizations of the Kitaev honeycomb model is often complicated by non-trivial interactions inherent to potential spin liquid candidates, where the interplay of exotic forms of quantum magnetism often leads to false indications of novel spin excitations. In this letter, we propose several distinct thermodynamic signatures of massive, itinerant Majorana fermions within the well-established analytical paradigm of Landau-Fermi liquid theory. We find that all salient features of the theory are confirmed in the specific heat measurements of the Kitaev spin liquid candidate Ag$_3$LiIr$_2$O$_6$. Our study is the first of its kind to present strong evidence for a Fermi liquid-like ground state in the fundamental excitations of a honeycomb iridate, and opens new experimental avenues to detect itinerant Majorana fermions in condensed matter as a whole.
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