On the generic increase of entropy in isolated systems
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914255820816384 |
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| author | Huang, Zhiqiang Cai, Qing-yu |
| author_facet | Huang, Zhiqiang Cai, Qing-yu |
| contents | This study establishes a universal mechanism for entropy production in isolated quantum systems governed by interactions that induce random-phase fluctuations. By developing a resolvent-based framework, we demonstrate that steady-state entropy generically arises from many-body interactions, independent of specific coupling details, provided the coherent accumulation of systematic biases does not overwhelm the random-phase fluctuations. Analytical arguments reveal that entropy generation is driven by two universal pathways: interaction-induced energy broadening and temporal coarse-graining over exponentially small energy gaps. To quantitatively capture the probability distribution, we introduce a hierarchical ansatz approach. A Lorentzian ansatz models the bulk region, leading to self-consistent equations for the broadening and shift parameters, and yields a logarithmic entropy scaling with interaction strength. For the tail behavior, a Gaussian ansatz is formulated, and the corresponding self-consistent condition is derived and validated. By further combining these profiles into an enhanced Lorentzian-Gaussian hybrid ansatz, we achieve a unified and refined description of the full distribution. Numerical simulations of nonintegrable Ising spin chains confirm the predicted logarithmic entropy scaling and validate the self-consistent equations. Our framework effectively bridges the concepts of observational entropy and von Neumann entropy dynamics, providing predictive tools for thermodynamic behavior in quantum many-body systems. These results resolve longstanding debates about interaction-dependent entropy scaling and offer pathways for entropy control in quantum technologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the generic increase of entropy in isolated systems Huang, Zhiqiang Cai, Qing-yu Quantum Physics Statistical Mechanics This study establishes a universal mechanism for entropy production in isolated quantum systems governed by interactions that induce random-phase fluctuations. By developing a resolvent-based framework, we demonstrate that steady-state entropy generically arises from many-body interactions, independent of specific coupling details, provided the coherent accumulation of systematic biases does not overwhelm the random-phase fluctuations. Analytical arguments reveal that entropy generation is driven by two universal pathways: interaction-induced energy broadening and temporal coarse-graining over exponentially small energy gaps. To quantitatively capture the probability distribution, we introduce a hierarchical ansatz approach. A Lorentzian ansatz models the bulk region, leading to self-consistent equations for the broadening and shift parameters, and yields a logarithmic entropy scaling with interaction strength. For the tail behavior, a Gaussian ansatz is formulated, and the corresponding self-consistent condition is derived and validated. By further combining these profiles into an enhanced Lorentzian-Gaussian hybrid ansatz, we achieve a unified and refined description of the full distribution. Numerical simulations of nonintegrable Ising spin chains confirm the predicted logarithmic entropy scaling and validate the self-consistent equations. Our framework effectively bridges the concepts of observational entropy and von Neumann entropy dynamics, providing predictive tools for thermodynamic behavior in quantum many-body systems. These results resolve longstanding debates about interaction-dependent entropy scaling and offer pathways for entropy control in quantum technologies. |
| title | On the generic increase of entropy in isolated systems |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2505.23041 |