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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2511.00131 |
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| _version_ | 1866914206186471424 |
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| author | Kobayashi, Shuhei |
| author_facet | Kobayashi, Shuhei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Three-Particle Dynamics to the Structural Origin of the Arrow of Time in Classical and Quantum Mechanics Kobayashi, Shuhei Statistical 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. |
| title | From Three-Particle Dynamics to the Structural Origin of the Arrow of Time in Classical and Quantum Mechanics |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2511.00131 |