Shuhei Kobayashi | Searcharxiv

arXiv2025

From Three-Particle Dynamics to the Structural Origin of the Arrow of Time in Classical and Quantum Mechanics

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.

cond-mat.stat-mech↗

arXiv2025

Analysis of Three-Particle Elastic Collisions Using Newtonian Mechanics and Vector Geometry

We study one-dimensional elastic collisions of three point masses on a line under vacuum, with no triple collisions. We express momentum conservation in matrix form and analyze the composite map $D=D_{BC}D_{AB}$ and its powers $D^k$, which yield the velocities after any prescribed number of collisions for arbitrary mass ratios and initial data. After that, using vector $u$ on a plane $s^\perp$, the total number of collisions is \[ n\;=\;1+\Big\lfloor\tfrac{Ω-ϕ_{BC}}θ\Big\rfloor+\Big\lceil\tfrac{Ω-ϕ_{BC}}θ\Big\rceil, \] Through this concept, $D$ is recognised as giving $u$ a rotation with angle $θ$ which is determined by only mass ratios. And, we calculated energy transfer through collisions. With the work, we find that the change of energy is proportional to total momentum of two particles and average velocity of particles based on initial average velocity of A and B before collision.

physics.class-ph↗