Exact four-vector work distribution and covariant fluctuation theorems of work for a relativistic particle in an expanding piston
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| Format: | Preprint |
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2025
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| _version_ | 1866909024225591296 |
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| author | Shi, Tingzhang Qi, Chentong Quan, H. T. |
| author_facet | Shi, Tingzhang Qi, Chentong Quan, H. T. |
| contents | We investigate the non-equilibrium four-vector work in an expanding relativistic piston. We derive the exact work distribution in this pedagogical model and find that the joint distribution of four-vector work $(W^0, W^1)$ concentrates on the origin and some curves in the $(W^0, W^1)$ space, rather than being smoothly distributed. In the non-relativistic limit, our model consistently recovers the non-relativistic dynamics. We further demonstrate that the momentum component of four-vector work remains significant in both the Lorentz-relativistic and Galilean-relativistic frameworks. On top of the work distribution, we verify a family of covariant fluctuation theorems of work. In addition, we introduce a novel geometrical technique for analyzing the dynamics of relativistic collision processes, which can be straightforwardly extended to multi-dimensional piston models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_22431 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact four-vector work distribution and covariant fluctuation theorems of work for a relativistic particle in an expanding piston Shi, Tingzhang Qi, Chentong Quan, H. T. Statistical Mechanics Classical Physics We investigate the non-equilibrium four-vector work in an expanding relativistic piston. We derive the exact work distribution in this pedagogical model and find that the joint distribution of four-vector work $(W^0, W^1)$ concentrates on the origin and some curves in the $(W^0, W^1)$ space, rather than being smoothly distributed. In the non-relativistic limit, our model consistently recovers the non-relativistic dynamics. We further demonstrate that the momentum component of four-vector work remains significant in both the Lorentz-relativistic and Galilean-relativistic frameworks. On top of the work distribution, we verify a family of covariant fluctuation theorems of work. In addition, we introduce a novel geometrical technique for analyzing the dynamics of relativistic collision processes, which can be straightforwardly extended to multi-dimensional piston models. |
| title | Exact four-vector work distribution and covariant fluctuation theorems of work for a relativistic particle in an expanding piston |
| topic | Statistical Mechanics Classical Physics |
| url | https://arxiv.org/abs/2511.22431 |