Nonequilibrium Thermodynamics/Molecular Scattering

Paul Hunt

Professor

238 ADM

517-432-4499


Associate Vice-President


Research webpage


Primary Research Area

Physical (Ph)

Other Area(s) of Interest

Theoretical and Computational (Th)

Research

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.

Selected 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. 1995, 102, 4548.

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. 1995, 102, 4563.

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

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. 1993, 99, 3444.

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. 1993, 99, 3455.

CV

Associate Vice President for Research

B. S., 1975, Michigan State Univ.

Ph.D., 1978, Oxford Univ.

NSF Postdoctoral Fellow, 1978-79, Harvard Univ.

Awards/Honors

1978 Ph.D. Oxford University, England
1975 Bachelor of Science with High Honors Michigan State University
0 Phi Beta Kappa Phi Beta Kappa
0 Rhodes Scholar
0 National Merit Scholar
0 NSF National Needs Postdoctoral Fellowship National Science Foundation
0 Phi Kappa Phi Phi Kappa Phi