NONEQUILIBRIUM THERMODYNAMICS/MOLECULAR SCATTERING

Paul M. Hunt Professor and Vice Provost for Computing and Technology (b. 1953). B. S., 1975, Michigan State University; Ph.D., 1978, Oxford University; NSF Postdoctoral Fellow, 1978-79, Harvard University. 517-353-0722 pmhunt@msu.edu

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 df. The quantity df 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 df is, in general, not a state function, but it is when the system exhibits detailed balance. In contrast, the function f_det obtained by integrating df along deterministic kinetic trajectories is a state function, as well as an identifiable term in the time-integrated dissipation. Unlike the total integrated dissipation, f_det remains finite during the infinite duration of the system’s relaxation to a non-equilibrium steady state, and hence f_det can be used to characterize that process. The variational relation df ³ 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 f_det 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 P_S = N exp(- f/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.

Representative Publications

Thermodynamic and Stochastic Theory of Nonequilibrium Systems: Fluctuation Probabilities and Excess Work, B. Peng, K. L. C. Hunt, P. M. Hunt, A. Suárez, and J. Ross, J. Chem. Phys., 102, 4548 (1995).

Thermodynamic and Stochastic Theory of Nonequilibrium Systems: A Lagrangian Approach to Fluctuations and Relation to Excess Work, A. Suárez, J. Ross, B. Peng, K. L. C. Hunt, and P. M. Hunt, J. Chem. Phys., 102, 4563 (1995).

Large Fluctuations and Optimal Paths in Chemical Kinetics, M. I. Dykman, E. Mori, J. Ross, and P. M. Hunt, J. Chem. Phys., 100, 5735 (1994).

Thermodynamic and Stochastic Theory of Reaction-Diffusion Systems with Multiple Stationary States, X. L. Chu, J. Ross, P. M. Hunt, and K. L. C. Hunt, J. Chem. Phys., 99, 3444 (1993).

Tests of Thermodynamic Theory of Relative Stability in One-Variable Systems, A. N. Wolff, A. Hjelmfelt, J. Ross, and P. M. Hunt, J. Chem. Phys., 99, 3455 (1993).