P systems with energy accounting

We consider P systems where each evolution rule "produces" or "consumes" some quantity of energy, in amounts which are expressed as integer numbers. In each moment and in each membrane the total energy involved in an evolution step should be positive, but if "too much" energy is present in a membrane, then the membrane will be destroyed (dissolved). We show that this feature is rather powerful. In the case of multisets of symbol-objects we find that systems with two membranes and arbitrary energy associated with rules, or with arbitrarily many membranes and a bounded energy associated with rules, characterize the recursively enumerable sets of vectors of natural numbers (catalysts and priorities are used). In the case of string-objects we have only proved that the recursively enumerable languages can be generated by systems with arbitrarily many membranes and bounded energy; when bounding the number of membranes and leaving free the quantity of energy associated with each rule we have only generated all matrix languages. Several research topics are also pointed out.