Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference

Abstract

We postulate a principle stating that the initial condition of a physical system is typically algorithmically independent of the dynamical law. We discuss the implications of this principle and argue that they link thermodynamics and causal inference. On the one hand, they entail behavior that is similar to the usual arrow of time. On the other hand, they motivate a statistical asymmetry between cause and effect that has recently been postulated in the field of causal inference, namely, that the probability distribution ${P}_{{\rm{cause}}}$ contains no information about the conditional distribution ${P}_{{\rm{effect}}| {\rm{cause}}}$ and vice versa, while ${P}_{{\rm{effect}}}$ may contain information about ${P}_{{\rm{cause}}| {\rm{effect}}}$ .

Keywords

• arrow of time
• causal inference
• Kolmogorov complexity
• physical entropy
• algorithmic randomness