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The interplay between cycle geometry and performance of sudden refrigerators

The relation between the geometry of refrigeration cycles and their performance is explored. The model studied is based on a coupled spin system. Small cycle times termed sudden refrigerators, develop coherence and inner friction. We explore the interplay between coherence and energy of the working medium employing a family of sudden cycles with decreasing cycle times. At the point of minimum ratio between energy and coherence the cycle changes geometry. This region of cycle times is characterised by short circuit cycles where heat is dissipated both to the hot and cold baths. We rationalise the cycle change of geometry as a result of a half integer quantisation which maximises coherence. From this point on, increasing or decreasing the cycle time, eventually leads to refrigeration cycles. The transition point between refrigerators and short circuit cycles is characterised by a transition from finite to singular dynamical temperature. Extremely short cycle times reach a universal limit where all cycles types are equivalent.