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In real-life statistical data, it seems that conditional probabilities forthe effect given their causes tend to be less complex and smoother thanconditionals for causes, given their effects. We have recently proposed andtested methods for causal inference in machine learning using a formalizationof this principle.  Here we try to provide some theoretical justification for causal inferencemethods based upon such a ``causally asymmetric'' interpretation of Occam'sRazor. To this end, we discuss toy models of cause-effect relations fromclassical and quantum physics as well as computer science in the context ofvarious aspects of complexity.  We argue that this asymmetry of the statistical dependences between cause andeffect has a thermodynamic origin. The essential link is the tendency of theenvironment to provide independent background noise realized by physicalsystems that are initially uncorrelated with the system under considerationrather than being finally uncorrelated. This link extends ideas from theliterature relating Reichenbach's principle of the common cause to the secondlaw.

On causally asymmetric versions of Occam's Razor and their relation to thermodynamics