His additional innovative ideas during that period include the use of Monte Carlo sampling as a computationally feasible means of estimating the uncertainty of weather forecasts, and the application of the fluctuation-dissipation theorem for estimating the climate response of the atmosphere.

Their topics include fluctuating hydrodynamics and fluctuation-dissipation theorem in equilibrium systems, non-equilibrium thermodynamics for evaporation and condensation, non-equilibrium thermodynamics of interfaces between aqueous solutions and crystals, minimizing entropy production with optimal control theory, mesoscopic non-equilibrium thermodynamics in biology, and the dynamics of complex fluid-fluid interfaces.

The random force [eta](t) is zero-centered and stationary Gaussian that obeys the generalized second fluctuation-dissipation theorem [67]:

When the internal noise [eta](t) in the generalized Langevin equation (9) is fractional Gaussian noise with correlation function (5), from the fluctuation-dissipation theorem (2), we derive the power-law memory kernel K(t) presented by Hurst exponent H, 0 < H < 1:

Physically such a friction term has, due to the fluctuation-dissipation theorem, its origin in a non-Ohmic thermal bath, whose influence on the dynamical system is described with a powerlaw correlated additive noise in the GLE, e.g., with fractional Gaussian noise which is closely related to fractional Brownian motion [15,17].

It can be shown that, in order to maintain a well defined temperature by way of consistency with a fluctuation-dissipation theorem [3], coefficients describing the strength of the dissipative and random forces must be coupled.