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 polytropic index, 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 presence of the magnetic field of varying strength. Further to understand the system dynamics under equilibrium and non-equilibrium conditions, the effect of non-extensive parameter ($q$) on the above observables is also studied.
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