Local dissipative Hamiltonian description of reversible reaction networks

In this letter we show that closed reversible chemical reaction networks with independent elementary reactions admit a global pseudo-Hamiltonian structure which is at least locally dissipative around any equilibrium point. The structure matrix of the Hamiltonian description reflects the graph topology of the reaction network and it is a smooth function of the concentrations of the chemical species in the positive orthant. The physical interpretation of the description is briefly explained and two illustrative examples are presented for global and local dissipative Hamiltonian description, respectively.