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The D-CTC condition, introduced by David Deutsch as a condition to befulfilled by analogues for processes of quantum systems in the presence ofclosed timelike curves, is investigated for classical statistical (non-quantum)bi-partite systems. It is shown that the D-CTC condition can generically befulfilled in classical statistical systems, under very general,model-independent conditions. The central property used is the convexity andcompleteness of the state space that allows it to generalize Deutsch's originalproof for q-bit systems to more general classes of statistically describedsystems. The results demonstrate that the D-CTC condition, or the conditionsunder which it can be fulfilled, is not characteristic of, or dependent on, thequantum nature of a bi-partite system.

The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems