  We study the thermodynamic analysis and logarithm corrections of the new
Schwarzschild black hole. We compute the thermodynamic quantities like entropy,
Hawking temperature and heat capacity. The area of black holes never decreases
because they absorb everything from their surroundings due to high gravity. In
this regard, the area-entropy relation proposed by Bekenstein needs to be
corrected, leading to the concept of logarithmic corrections. To do so, we
obtain the corrected entropy for new Schwarzschild black hole to analyze the
effects of thermal fluctuations and we evaluate the thermodynamic quantities
like specific heat, internal energy, Helmholtz free energy, Gibbs free energy,
enthalpy and pressure in the presence of correction parameter $\eta$.
Furthermore, we check the stability of the system with the help of heat
capacity and well known Hessian matrix technique. By our graphical analysis, we
observe that the thermal fluctuations effects the stability of small radii
black holes (e.g., New Schwarzchild black hole) and therefore, small black
holes get unstable regions due to these first order corrections.
