On fluctuations in liquids and gases

The Lagrangian formalism is used to derive a system of nonlinear inhomogeneous dissipative differential equations describing the nonlinear dynamics of interrelated fluctuations of density, δρ, and temperature, δT, in a medium. With these equations, the unstable (with respect to initial conditions) phase trajectory describing parameter fluctuations in the ρ-T plane was obtained. By numerically solving the equations, we show that δρ and δT oscillate in time almost periodically, which is typical of fluctuations.