No mysterious motor driving time forward Multiple paths of randomness toward time irreversibility

Pas de moteur mystérieux du temps De la multiplicité de chemins des mouvement aléatoires à la preuve mathématique de la flèche du temps

Qiuping A. Wang (1, 2) , Qiong Ye (1)

1 IMMM - Institut des Molécules et Matériaux du Mans
2 ESIEA - Ecole Supérieure d'Informatique Electronique Automatique [Paris]

In this work, I address the century old conflict between the reversible time of classical physics and the irreversible time we observe and experience every day. I formulate a mathematical proof of time irreversibility starting from the reversible time of physics. The key point is a mathematical definition of time, the first one in the history of physics, which implements the intuitive idea that time is an attribute of movement, leading to a relationship between time and path of motion. By considering fundamental principle of dynamics, it is shown that time is necessarily reversible in deterministic motion having unicity of path with given initial condition, and becomes irreversible in indeterministic (random) motion having multiplicity of paths. The proof of this irreversibility is worked out by considering the path probability as well as the path entropy, a measure of probabilistic uncertainty of path of random motion, which turns out to be increasing function of time, and an indicator of the time arrow pointing in the direction of increasing randomness and disorder.

Mots clés: Time; space; irreversibility; entropy; random dynamics; path probability; information

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique Classique [physics.class-ph]

Qiuping A. Wang, Qiong Ye. No mysterious motor driving time forward Multiple paths of randomness toward time irreversibility. 2022. ⟨hal-03354947v6⟩