Irreversible thermodynamics of chemical neural networks is formulated, and energy and matter dissipation accompanying logic operations is investigated in this paper. This formalism therefore puts the dynamics of neural networks within the framework of the laws of thermodynamics and thereby provides a mathematical basis to study neural dynamics as irreversible processes subjected to the thermodynamic principles. By using the minimal bromate oscillator, we apply the formalism of irreversible thermodynamics to study numerically the modes of energy dissipation related to logic operations. The calortropy of the system serves as an integral surface of the evolution equations for the concentrations of chemical species in the neurons of the network. It is shown that logic operations in the neural networks can be regarded as evolution of the states of neurons in the network toward the steady-state values of the calortropy production characteristic of the logic operations.