  We find the Euler-Lagrangian equation by maximising the total entropy. Hence
we obtain an expression for mass of the spherically symmetric system by solving
the Euler-Lagrangian equation where the Homotopy Perturbation Method has been
employed. With the help of this expression and the Einstein field equations we
obtain an interior solution set. Thereafter, we explain different aspects of
the solution describing the system in connection to the mass, density,
pressures, energy, stability, mass-radius ratio, compactness factor and surface
redshift. This analysis shows that all the physical properties, in connection
to brown dwarf stars, are valid with the observed features.
