On the absence of time-translation symmetry breaking in some non-reversible interacting particle systems
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911468590465024 |
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| author | Köppl, Jonas |
| author_facet | Köppl, Jonas |
| contents | The conditions under which stochastic systems of infinitely many interacting particles can maintain sufficient spatial order to move coherently along a time-periodic orbit, thereby breaking the time-translation invariance of the underlying dynamical equation, have been an elusive issue. Via a free energy technique, we prove that if a non-reversible interacting particle system on $\mathbb{Z}^d$, $d=1,2$, with strictly positive rates admits a product measure as a stationary measure, then it cannot exhibit time-periodic behaviour. This provides a first step towards a general conjecture that time-periodic behaviour cannot occur in one- and two-dimensional systems with short-range interactions and constitutes the first result for non-reversible dynamics in dimension two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22104 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the absence of time-translation symmetry breaking in some non-reversible interacting particle systems Köppl, Jonas Probability Mathematical Physics Primary 82C22, Secondary 60K35 The conditions under which stochastic systems of infinitely many interacting particles can maintain sufficient spatial order to move coherently along a time-periodic orbit, thereby breaking the time-translation invariance of the underlying dynamical equation, have been an elusive issue. Via a free energy technique, we prove that if a non-reversible interacting particle system on $\mathbb{Z}^d$, $d=1,2$, with strictly positive rates admits a product measure as a stationary measure, then it cannot exhibit time-periodic behaviour. This provides a first step towards a general conjecture that time-periodic behaviour cannot occur in one- and two-dimensional systems with short-range interactions and constitutes the first result for non-reversible dynamics in dimension two. |
| title | On the absence of time-translation symmetry breaking in some non-reversible interacting particle systems |
| topic | Probability Mathematical Physics Primary 82C22, Secondary 60K35 |
| url | https://arxiv.org/abs/2602.22104 |