Is there any reported organic reaction which forms product on standing without any extrnal energy source eg. without stirring, without heating, without catalyst? Is there any specific name for such kind of reactions?
The statement is poorly formulated. Catalyst do not provide the energy source, but lowers the activation barrier for the reaction.
As about reaction without thermal energy: this indeed happens thanks to zero-point energy contribution, but I am not aware of any organic chemistry application besides certain plastics (especially polyimides) which remain flexible down to absolute zero.
Food and medical products undergo aging with no external contributions. The studies of them are required to determine the safe shelf life and termination date.
Any reaction that results in a net increase in total entropy will occur without any external help. It will occur to the the same extent with or without a catalyst, but will occur faster with a catalyst than without it. An increase in total entropy is equated with a decrease in the Helmholtz free energy if the system is maintained at constant volume and with a decrease in the Gibbs free energy if it is maintained at constant pressure (temperature assumed constant, or at least equal in the initial and final states, in both cases).
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