{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:55:43Z","timestamp":1740149743387,"version":"3.37.3"},"reference-count":77,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,11]],"date-time":"2018-10-11T00:00:00Z","timestamp":1539216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000925","name":"John Templeton Foundation","doi-asserted-by":"publisher","award":["60230"],"id":[{"id":"10.13039\/100000925","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"Recently, the properties of bouncing oil droplets, also known as \u201cwalkers,\u201d have attracted much attention because they are thought to offer a gateway to a better understanding of quantum behavior. They indeed constitute a macroscopic realization of wave-particle duality, in the sense that their trajectories are guided by a self-generated surrounding wave. The aim of this paper is to try to describe walker phenomenology in terms of de Broglie\u2013Bohm dynamics and of a stochastic version thereof. In particular, we first study how a stochastic modification of the de Broglie pilot-wave theory, \u00e0 la Nelson, affects the process of relaxation to quantum equilibrium, and we prove an H-theorem for the relaxation to quantum equilibrium under Nelson-type dynamics. We then compare the onset of equilibrium in the stochastic and the de Broglie\u2013Bohm approaches and we propose some simple experiments by which one can test the applicability of our theory to the context of bouncing oil droplets. Finally, we compare our theory to actual observations of walker behavior in a 2D harmonic potential well.<\/jats:p>","DOI":"10.3390\/e20100780","type":"journal-article","created":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T06:58:04Z","timestamp":1539327484000},"page":"780","source":"Crossref","is-referenced-by-count":8,"title":["Bouncing Oil Droplets, de Broglie\u2019s Quantum Thermostat, and Convergence to Equilibrium"],"prefix":"10.3390","volume":"20","author":[{"given":"Mohamed","family":"Hatifi","sequence":"first","affiliation":[{"name":"Aix Marseille Universit\u00e9, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, 13013 Marseille, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8054-0239","authenticated-orcid":false,"given":"Ralph","family":"Willox","sequence":"additional","affiliation":[{"name":"Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan"}]},{"given":"Samuel","family":"Colin","sequence":"additional","affiliation":[{"name":"Centro Brasileiro de Pesquisas F\u00edsicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil"}]},{"given":"Thomas","family":"Durt","sequence":"additional","affiliation":[{"name":"Aix Marseille Universit\u00e9, CNRS, Centrale Marseille, Institut Fresnel UMR 7249, 13013 Marseille, France"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15410","DOI":"10.1103\/PhysRevLett.97.154101","article-title":"Single-Particle Diffraction and Interference at a Macroscopic Scale","volume":"97","author":"Couder","year":"2006","journal-title":"Phys. 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