The counter-intuitive statistics of thermodynamics on a microscopic scale

The counter-intuitive statistics of thermodynamics on a microscopic scale

Mon, 09/09/2024

Publication

Publication of the Physics Laboratory in the Physical Review Letters on July 31, 2024. Communication by CNRS Physics on September 2, 2024.

Experiments on a classical microscopic system show that, while the second principle of thermodynamics is still valid on average, it can be circumvented experimentally in 95% of cases! A study conducted at the Physics Laboratory of ENS de Lyon, published in Physical Review Letters.

Abstract

We demonstrate experimentally that, applying optimal protocols that drive the system between two equilibrium states characterized by a free energy difference Δ⁢𝐹, we can maximize the probability of performing the transition between the two states with a work 𝑊 smaller than Δ⁢𝐹. The second law holds only on average, resulting in the inequality ⟨𝑊⟩≥Δ⁢𝐹. The experiment is performed using an underdamped oscillator evolving in a double-well potential. We show that with a suitable choice of parameters the probability of obtaining trajectories with 𝑊≤Δ⁢𝐹 can be larger than 95%. Very fast protocols are a key feature to obtain these results, which are explained in terms of the Jarzynski equality.

figure
An oscillator explores a double well of asymmetric potential Uinitial(x) (green) under the effect of thermal agitation, and is statistically more often on the left, in the well of lower energy (Pinitial(x) position distribution, blue). By instantaneously modifying the potential towards more asymmetry (Ufinal(x), in red), we increase the free energy of system F. The work W performed in this operation is most often zero (oscillator to the left, W=0<∆F), and but its average is compensated for by experiments initiated with an oscillator to the right (W>0).
Credit: Ludovic Bellon

Reference
Probabilistic Work Extraction on a Classical Oscillator Beyond the Second Law. Nicolas Barros, Sergio Ciliberto, and Ludovic Bellon. Phys. Rev. Lett., July 31, 2024.
DOI : 10.1103/PhysRevLett.133.057101
Open archive arXiv: 10.48550/arXiv.2402.18556

Subject(s)
Affiliated Structures and Partners
Keywords