Raphael Chetrite - Laboratoire J.A. Dieudonné - Keywords: Second Law, Shannon Entropy

Raphael Chetrite - Laboratoire J.A. Dieudonné - Keywords: Second Law, Shannon Entropy

Contribution title: On Gibbs-Shannon Entropy

This talk will be focus on the question of the physical contents of the Gibbs-Shannon entropy outside equilibrium.

Article : Gavrilov-Chetrite-Bechhoeffer : Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs-Shannon. PNAS 2017

Significance : The second law of thermodynamics states that the total entropy of an isolated system is constant or increasing. This constrains the laws of physics, ruling out perpetual-motion machines that convert heat to work without any side effect. At its heart, the second law is a statement about entropy, yet entropy is an elusive concept: To date, it has not been directly measured but is rather inferred from other quantities, such as the integral of the specific heat over temperature. Here, by measuring the work required to erase a fraction of a bit of information, we isolate directly the change in entropy, showing that it is compatible with the functional form proposed by Shannon, demonstrating its physical meaning in this context.

Abstract: Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here we measure experimentally this function in a system that is in local but not global equilibrium. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a two-state system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds.