Virial Extension for Discrete Data Series

The Virial theorem has been applied with considerable success in various fields of natural sciences. This proposal shows its extension by applying it to discrete data series. This application will be called the Virial theorem extension and can be applied to the numerical solution of nonlinear dynamic systems represented by difference equations, such as logistic, discubic and random number generators. differential equations like the nonlinear double pendulum and series of pseudorandom numbers and its reciprocals. The results obtained show that the proposal characterizes and distinguishes different types of behavior from the series under study. It also shows great sensitivity to the evolution of the series, even anticipating critical points. The proposed method to construct the discrete Virial extension does not require the existence of a Hamiltonian, which allows its application to series obtained experimentally. For pseudorandom number series, the extension reveals a consistent, quasi-specular behavior between its kinetic and potential factors, suggesting an underlying structural property. From a general point of view, this research shows a series of properties that can be reinterpreted in light of the discrete Virial coefficient, providing a novel and versatile tool given its minimal applicability requirements.