Abstract

This talk is partly historical overview, partly a discussion of how different ‘interpretations’ of entropy give wildly different experimental predictions, and partly an account of the stochastic interpretation of the second law and its role in current research on active soft matter. The talk was originally prepared for an event marking the 200th Anniversary of Kelvin’s birth, June 26th 1824.

Kelvin’s statement of the second law was grounded in the macroscopic world of heat engines. It led to the thermodynamic concept of entropy—the second law being equivalent to a statement that the entropy in a closed system (or indeed, the universe) can only increase. This ‘universal principle of degradation’ applies only at macroscopic scales, as Kelvin made clear in 1874. In the intervening 150 years, work on mesoscopic systems, specifically colloidal suspensions, has led to crucial clarifications and extensions of the second law. The first instance was Perrin’s 1909 confirmation via colloidal sedimentation of Boltzmann’s statistical view of entropy (and with it the atomic theory of matter). Much later, the discovery in 1986 of colloidal crystals offers overlooked but decisive evidence that the statistical entropy is informatic rather than kinetic in character. Third, colloidal experiments were the first to confirm several powerful generalizations of the second law (formulated in the 1990s) known as ‘fluctuation theorems’. These quantify precisely how probable it is for entropy to decrease spontaneously ‘against the odds’. Finally, in the 21st Century, colloid scientists have turned their attention to self-propelled particles whose dynamics are irreversible at the smallest scales measurable. These ‘active matter’ systems create a new arena in which concepts such as entropy production can be explored at the mesoscale.