Irreversibility in Non-reciprocal Chaotic Systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929716495122432 |
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| author | Pham, Tuan Alonso, Albert Proesmans, Karel |
| author_facet | Pham, Tuan Alonso, Albert Proesmans, Karel |
| contents | How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent neural networks that undergoes a transition from quiescence to chaos at a critical heterogeneity. In the thermodynamic limit, using dynamical mean field theory, we obtain an exact expression for the averaged entropy production rate - a measure of irreversibility - for any heterogeneity level J. We show how this quantity becomes a constant at the onset of chaos while changing its functional form upon crossing this point. The latter can be elucidated by closed-form approximations valid for below and slightly above the critical point and for large J. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_17939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irreversibility in Non-reciprocal Chaotic Systems Pham, Tuan Alonso, Albert Proesmans, Karel Statistical Mechanics Disordered Systems and Neural Networks How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent neural networks that undergoes a transition from quiescence to chaos at a critical heterogeneity. In the thermodynamic limit, using dynamical mean field theory, we obtain an exact expression for the averaged entropy production rate - a measure of irreversibility - for any heterogeneity level J. We show how this quantity becomes a constant at the onset of chaos while changing its functional form upon crossing this point. The latter can be elucidated by closed-form approximations valid for below and slightly above the critical point and for large J. |
| title | Irreversibility in Non-reciprocal Chaotic Systems |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2407.17939 |