### Nonequilibrium Thermodynamics/Molecular Scattering

Professor

** ** 238 ADM

** ** 517-432-4499

Associate Vice-President

**Primary Research Area**

Physical (Ph)

**Other Area(s) of Interest**

Theoretical and Computational (Th)

### Research

(Research Description PDF)

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 P_{S} = 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 |