The name Boltzmann integral is used for two distinct integral constructions. In kinetic theory, the Boltzmann collision integral describes the net change in a particle distribution caused by collisions (Cercignani et al. 1994). In linear viscoelasticity, the Boltzmann superposition integral expresses a stress or strain response as a convolution over the loading history (Tschoegl 1989).
Boltzmann Integral
See also
Boltzmann Collision Integral, Boltzmann Superposition IntegralExplore with Wolfram|Alpha
References
Cercignani, C.; Illner, R.; and Pulvirenti, M. The Mathematical Theory of Dilute Gases. New York: Springer-Verlag, 1994. https://doi.org/10.1007/978-1-4419-8524-8.Tschoegl, N. W. The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction. Berlin, Germany: Springer-Verlag, 1989. https://doi.org/10.1007/978-3-642-73602-5.Cite this as:
Weisstein, Eric W. "Boltzmann Integral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BoltzmannIntegral.html