Condensed Matter Physics, 2013, vol. 16, No. 4, 430031-13
DOI:10.5488/CMP.16.43003           arXiv:1312.4409

Title: Time evolution of a small reactive system.
  J.P. Badiali (LECIME, ENSCP-Université Pierre et Marie Curie,CNRS/UMR7575 4 Place Jussieu, 75230 Paris Cedex 05, France)

We investigate the irreversible evolution of a small system in which a chemical reaction takes place. We have two main goals: the first requires to find an equation to produce a time-irreversible behavior,the second consists in introducing a simple exactly solvable model in order to understand basic facts in chemical kinetics. Our basic tool is the transition function counting the number of paths joining two points in the reactive coordinates system. An exact quantum Smoluchowski equation is derived for the reactive system in vacuum, in presence of a solvent in equilibrium at any time with the reactive system a new Smoluchowski equation is obtained. The transition from a quantum regime to a classical one is discussed. The case of a reactive system not in equilibrium with its neighborhood is investigated in terms of path integral and via a partial differential function. Memory effects and closure assumptions are discussed. Using a simple potential model the chemical rate constant is calculated exactly and questions such as the meaning of the activation energy or the physical content of the so-called prefactor are investigated.

Key words: : irreversibility, transition function, Smoluchowski equation, chemical rate constant,activation energy.
PACS: :03.65Ca, 05.30-d, 05.70-a, 47.53+n

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