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Updated: May 26, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Local kinetic interpretation of entropy production through reversed diffusion
A Porporato1, P R Kramer, M Cassiani
1Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina, USA. amilcare@duke.edu
Abstract:
The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching formula for the steady-state probability density function along with a geometric interpretation of the fluctuation-dissipation relation. Finally, the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties, and a stochastic differential equation for entropy production is obtained using the Girsanov theorem for reversed diffusion. The results are illustrated for the Ornstein-Uhlenbeck process.
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