1) The mathematical statement of the second law of thermodynamics is typically expressed in terms of entropy. It can be stated as: "In any natural or spontaneous process, the total entropy of a closed system and its surroundings always increases or remains constant but never decreases."
2) The mathematical statement of the second law of thermodynamics for a noncyclic process involves the concept of entropy change. It can be expressed as: "For a noncyclic process, the entropy change of a system and its surroundings combined is greater than or equal to zero."
3) The third part of your question seems to be incomplete. Could you please provide the complete question or any additional information related to it?