Dynamics and macroscopic properties of condensed matter systems can be formulated in the framework of C*-algebras. The linear and non-linear response functions to homogeneous fields can be often cast in the form of N-point correlation functions and these expressions are written directly in the thermodynamic limit. In this talk, I describe a generic set of ideas on how to obtain canonical finite-volume approximations for a class of C*-algebras (and of their non-commutative calculus). Through explicit error estimates, these finite-volume approximations can be shown to converge exponential fast to the thermodynamic limit. Examples will be provided.