Relation between entropy and diffusion

The diffusion constant of a liquid is a fundamental dynamic property which not only is a measure of the fluidity of the system but also is involved in many theoretical descriptions that involve molecular processes such as chemical reactions. An intriguing relationship between diffusion constant and entropy has become a subject of increasing scientific discussions in recent times. This has the potential for offering insight into the nature of both, especially that of a correlation between the structure and the dynamics. 

While Boltzmann s law related entropy to the number of microscopic states, this law is strictly valid only at constant energy where the ergodicity of the system ensures that given sufficient time the system visits all the microscopic states. Experimental systems are, however, not at constant energy or volume, so Boltzmann s law, however elegant, is not directly useful to us. 

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