(untitled) (London Journal of Research In Science: Natural and Formal, 2025)
This paper is concerned with an extension of the fluctuation-dissipation (F-D) relations proposed by J. von Neumann and D. Grady for the shock compression of hydrodynamic solids by use of an underlying probability density distribution. As a specific illustration of the extension, a beta function is used to develop probabilistic F-D relations. Usefulness of the extension is evaluated in prediction of Pop-plot power coefficients in the pressure-time domain. Predicted values are found to be in a reasonable agreement with measured values. Additional results include a pressure threshold for the appearance of a uniform probability distribution of energy fluctuations and the upper limit of dissipated kinetic energy.