This thesis includes three parts . Thermodynamics curvature of 2d-Ising model on Kagome lattice considered in first part . According to the standard scaling hypothesis , thermodynamics curvature at critical point behaves aswhere is heat capacity critical exponent and denotes the critical temperature . While it is true for systems with positive value of and some systems with zero value of , it is not verified for negative value of and it bahaves asfor these systems . Here we derive thermodynamics curvature of a system with zero value of and find that it behaves like negative . According to the results exist for different systems , it seems that the behaviour of thermodynamics curvature depends on dimension as well as the sign of . Second part introduces a local dissipation theorem. A standard method for measuring traort properties in simulation is the transient time correlation function that represents a special case of a more general theorem, the dissipation theorem. It is indirectly calculates phase function averages and these averages often have significantly less statistical error than direct averages. A local version of fluctuation theorem has been recently demonstrated. Here we show that a similar local expression can be obtained for dissipation theorem, providing a way of determining values of phase functions by monitoring the fluctuations of phase functions in a small region of the system. An ideal gas obeying non-abelian statistics at condensation point is investigated in the last part. Its thermodynamics quantities are derived. It is found that thermodynamics quantities are finite at condensation point while their derivatives diverge at this point and behave as ear the condensation point where is a critical exponent. Critical exponents related to the heat capacity () and the compressibility () are obtained by fitting numerical results and other critical exponents are also obtained by using the scaling law hypothesis for a three dimensional non-abelian gas. This set of critical exponents introduces a new universality 7.5pt; HEIGHT: 16.5pt" , thermodynamics curvature behaves like in three dimensions and behaves like in four dimensions. The result of first part and current part reveal that the scaling behaviour of thermodynamics curvature depends on dimensions as well as the sign of critical exponent .