Thermodynamics of chaotic relaxation processes

The established thermodynamic formalism of chaotic dynamics,valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the phase-space average of an integrated observable (e.g. Lyapunov exponent, diffusion coefficient) is obtained for finite time. Most notably, the thermodynamic treatment may predict the finite-time distributions of any integrated observable from the leading and subleading eigenfunctions of the Perron-Frobenius/Koopman transfer operator. Examples of that equivalence are shown, and the theory is tested numerically in three paradigms of chaos.