Stochastic thermodynamics and predictability of Ornstein-Uhlenbeck processes: an application to the Madden-Julian Oscillation

Abstract

Climate oscillations are intrinsically out-of-equilibrium phenomena, yet the connection between their predictability and nonequilibrium thermodynamic properties remains unexplored. We develop a coarse-grained stochastic thermodynamic framework for Ornstein-Uhlenbeck (OU) processes and apply this framework to climate data via linear inverse models (LIMs), linking predictability, entropy production, dynamical activity, and path action. Climate oscillations are often studied in a 2d phase space of climate indices, which are even under time-reversal, motivating our focus on 2d OU dynamics with even variables. We find that coordinate-invariant properties of 2d OU processes can be reduced to a minimal three-parameter description: two diffusivities and a phase-space rotation. We show that these quantities fundamentally characterize distinct aspects of the dynamics. We find that higher irreversibility and dynamical activity do not necessarily imply reduced predictability. Rather, it is the path action which is most closely connected to a commonly used measure of predictability, the anomaly correlation coefficient (ACC). As an illustrative example, we apply this framework to the Madden-Julian Oscillation (MJO) over the twentieth century. We find that the MJO has become simultaneously more predictable, as seen previously, while at the same time becoming more irreversible and more active. Predictability is driven predominantly by the reduced mean diffusion. Entropy production reflects the combined evolution of all three parameters. These results suggest that stochastic thermodynamics provides a powerful lens for studying nonequilibrium climate phenomena.