2025/10/31 by Kobayashi, Shuhei
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum chaos and dynamical systems #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2511.00131
openalex publication_date 2025/10/31 · openalex created_date 2025/11/05 · openalex updated_date 2026/07/31
This paper presents a unified formulation of the origin of the arrow of time in classical and quantum mechanics. We begin with a mechanical analysis of a one-dimensional three-particle system, which provides a concrete example in which macroscopic irreversibility emerges despite microscopically reversible dynamics. By abstracting this mechanism, we identify coarse-graining as the essential ingredient responsible for macroscopic time asymmetry. We then formulate a general structural criterion for the thermodynamic arrow of time. We show that when microscopic time evolution forms a group while the induced macroscopic evolution forms only a semigroup, macroscopic time-reversal symmetry is necessarily broken. We prove that this semigroup structure arises if and only if the coarse-graining map from microscopic to macroscopic states is non-injective. This result holds independently of whether the underlying system is classical or quantum. In the quantum case, using density matrices, antiunitary time reversal, and CPTP coarse-graining maps, we show that macroscopic irreversibility follows inevitably from information loss, without requiring any asymmetry in the microscopic laws. Our results demonstrate that the thermodynamic arrow of time has a universal structural origin: the loss of microscopic information inherent in coarse-graining.