  Non-central heavy-ion collisions at ultra-relativistic energies are unique in
producing magnetic fields of the largest strength in the laboratory. Such
fields being produced at the early stages of the collision could affect the
properties of Quantum Chromodynamics (QCD) matter formed in the relativistic
heavy-ion collisions. The transient magnetic field leaves its reminiscence,
which in principle, can affect the thermodynamic and transport properties of
the final state dynamics of the system. In this work, we study the
thermodynamic properties of a hadron gas in the presence of an external static
magnetic field using a thermodynamically consistent non-extensive Tsallis
distribution function. Various thermodynamical observables such as energy
density ($\epsilon$), entropy density ($s$), pressure ($P$) and speed of sound
($c_{\rm s}$) are studied. Investigation of magnetization ($M$) is also
performed and this analysis reveals an interplay of diamagnetic and
paramagnetic nature of the system in the presence of a magnetic field of
varying strength. Further, to understand the system dynamics under equilibrium
and non-equilibrium conditions, the effect of the non-extensive parameter ($q$)
on the above observables is also studied.
