Conduction and chaotic dynamics

In this work we analyze the Onsager theory of conduction within the context of lowdimensional nonlinear systems. After presenting the thermodynamics of conductive processes, we introduce the logistic map as a paradigmatic example for non-conservative chaotic dynamics. In the fully chaotic case, when the logistic map coincides with the Ulam map, we exactly characterize the exponential regression to equilibrium of a uniformly distributed set of initial values of particle positions. This new approach gives rise to the question of whether the Onsager theory could be generalized by introducing an adapted concept of microscopic reversibility.