  The theory of computation is based on abstract computing automata which can
be classified into a three-class hierarchy: Finite Automata (FA), Push-down
Automata (PDA) and the Turing Machines (TM). Each class corresponds to
grammar/language classes. The function of the automata consists on recognizing
words in a language generated by some grammar and expressed with letters from
an alphabet. Such automata are, in principle, abstract entities and with
suitable combinations of them we can represent any computation, no matter how
complex. Their physical implementations are possible in any information
carrying and recognition contexts and media, such as electrons in
semiconductors, certain biomolecules in biology or even non-biological
molecules. Here we describe and build non-biochemistry (inorganic chemistry)
examples of a FA, PDA and TM computations carried out by specific laboratory
realizations of the automata. For each of the three realizations we find a
thermodynamic metric, based on enthalpy for the FA and PDA, and on the Gibbs
free energy for the TM, to both assess the results of computation and as a
first step towards quantifying the energetic cost of such computations.
