Linear optimal protocol for physical constraints in weakly driven processes
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916073991831552 |
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| author | Nazé, Pierre |
| author_facet | Nazé, Pierre |
| contents | The minimization of irreversible work in weakly driven systems within linear response under physical constraints on the protocol derivative is studied. The problem reduces to a shifted eigenvalue equation involving the relaxation function. Owing to its dependence on time differences and its evenness, the relaxation kernel is naturally defined over a symmetric interval, where a periodic representation arises as a consistent closure that restores continuous translational invariance. Also, it shows how the irreversible work is defined in practice. Within this framework, the operator becomes diagonal in a Fourier basis. The global optimal solution is the zero mode, yielding a constant driving speed and a linear protocol. The corresponding optimal work depends only on the integrated relaxation function. Numerical results obtained via genetic programming confirm the robustness of this solution across different kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear optimal protocol for physical constraints in weakly driven processes Nazé, Pierre Statistical Mechanics The minimization of irreversible work in weakly driven systems within linear response under physical constraints on the protocol derivative is studied. The problem reduces to a shifted eigenvalue equation involving the relaxation function. Owing to its dependence on time differences and its evenness, the relaxation kernel is naturally defined over a symmetric interval, where a periodic representation arises as a consistent closure that restores continuous translational invariance. Also, it shows how the irreversible work is defined in practice. Within this framework, the operator becomes diagonal in a Fourier basis. The global optimal solution is the zero mode, yielding a constant driving speed and a linear protocol. The corresponding optimal work depends only on the integrated relaxation function. Numerical results obtained via genetic programming confirm the robustness of this solution across different kernels. |
| title | Linear optimal protocol for physical constraints in weakly driven processes |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2606.01988 |