A perpetual motion machine of the first sort is a device that defies the First Law of Thermodynamics by producing energy.
The second law's validity is statistical rather than mathematical because it rests on the fact that the bodies we deal with are made up of millions of molecules. Because of this, any efficiency tiny set of molecules consistently and significantly violates the first law of thermodynamics. The second law of thermodynamics is broken by a heat engine that claims to be more efficient than the Carnot efficiency. The first law clearly states that no apparatus that produces heat or meaningful work can exist without using energy from some source. Since it was established 140 years ago, there have never been any exceptions to this rule. These kinds of machines are unreal and go against the first law of thermodynamics. The first law of thermodynamics has a flaw in that it says nothing about the direction in which heat flows. No efficiency is given as to whether the procedure is spontaneous or not. The process cannot be reversed. In reality, not all of the heat is converted into work.
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