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Paul Hunt

Photo of Paul Hunt


Nonequilibrium Thermodynamics/ Molecular Scattering

A continuing research collaboration exists with Katharine Hunt and John Ross (Stanford). We are pursuing a global thermodynamic and stochastic theory of open chemical systems far from equilibrium. Recently, we analyzed a broad class of isothermal, multi-component reaction mechanisms with multiple steady states, studied under the assumption of local equilibrium. We generalized species-specific affinities of reaction intermediates in open systems, obtained in our prior work for non-autocatalytic reaction mechanisms, to autocatalytic kinetics and we defined with these affinities an “excess” free energy differential dφ. The quantity dφ is the difference between the work required to reverse a spontaneous concentration change and the work available when the same concentration change is imposed on a system in a reference steady state. The integral of dφ is, in general, not a state function, but it is when the system exhibits detailed balance. In contrast, the function φdet obtained by integrating dφ along deterministic kinetic trajectories is a state function, as well as an identifiable term in the time-integrated dissipation. Unlike the total integrated dissipation, φdet remains finite during the infinite duration of the system’s relaxation to a non-equilibrium steady state, and hence φdet can be used to characterize that process. The variational relation dφ ≥ 0 is a necessary and sufficient thermo­­dynamic criterion for a stable steady state, in terms of the excess work of displacement of the intermediates, and φdet is a Liapunov function in the domain of attraction of such steady states. An interesting connection exists between the non-equilibrium thermodynamics and stochastic theory. For equilibrating and non-autocatalytic systems, the stationary distribution of the master equation may be obtained in the form PS = N exp(-φ/kT). This generalizes the Einstein fluctuation formula to multivariable systems with detailed balance, far from equilibrium. Most recently, attention has centered on study of systems with stable limit cycles. Long-standing interest in molecular scattering problems continues, especially in those involving dissociative processes.