The Causal Second Law

I argue that if a special science satisfies certain key assumptions that are familiar from physicalist accounts of the special sciences and from physics, then its causal regularities have an associated notion of entropy, and that this causal entropy cannot decrease from a robust cause to its effect. Due to its analogy with the second laws of thermodynamics and statistical physics, I call the latter conclusion the causal second law. In this paper, I clarify the key assumptions, prove the causal second law, give sufficient conditions for causal entropy increase, relate the causal second law to statistical mechanics and thermodynamics, and argue that the reversibility objection does not threaten it. In addition, I claim that the causal second law is compatible with a non-metaphysical understanding of supervenience and the open systems view, argue that it does not imply a causal time arrow, reflect on relaxing the robustness condition, question whether it is necessary to invoke thermodynamics to show that special sciences' time arrows exist, and discuss a transition-relative-frequency-based, special-science-internal characterization of causal regularities.