Causal inference rules for algorithmic dependences and why they reproduce the arrow of time

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The causal Markov condition relates statistical dependences to causality. Its relevance is meanwhile widely appreciated in machine learning, statistics, and physics. I describe the *algorithmic* causal Markov condition relating algorithmic dependences to causality, which can be used for inferring causal relations among single objects without referring to statistics. The underlying postulate "no algorithmic dependence without causal relation" extends Reichenbach's Principle to a probability-free setting. I argue that a related postulate called "algorithmic independence of initial state and dynamics" reproduces the non-decrease of entropy according to the thermodynamic arrow of time.