Causality, response theory, and the second law of thermodynamics

We show that there is a close connection between the assumption of causality and the second law of thermodynamics. We also show that for a class of classical reversible deterministic systems it is overwhelmingly improbable either to find causal steady states that violate the second law, or anticausal states that satisfy the second law. These arguments indicate that the existence of (and the sign associated with) the second law of thermodynamics is ultimately determined by causality. Our discussion employs a Green-Kubo relation that we derive for an anticausal linear transport coefficient.