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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.23698 |
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| _version_ | 1866917972396736512 |
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| author | Theurel, David |
| author_facet | Theurel, David |
| contents | Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove a thermodynamic limitation on the information that can be obtained about a classical system by means of observations: A direct analogue of the Robertson-Schrödinger quantum uncertainty relation controls the acquisition of information at the classical microscale. Central to this theorem is the notion of the "quality" of a measuring probe; a temperature-dependent strictly positive quantity that serves as a figure of merit of the probe, and that plays the role of $1/\hbar$ in the classical uncertainty relation. This study sets the stage for a new area of research into resource theories of classical measurement, in which high-quality measurements and high-information states of knowledge are the limited resources. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The limits of knowledge in classical physics resemble the quantum uncertainty relation Theurel, David Statistical Mechanics Classical Physics Quantum Physics Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove a thermodynamic limitation on the information that can be obtained about a classical system by means of observations: A direct analogue of the Robertson-Schrödinger quantum uncertainty relation controls the acquisition of information at the classical microscale. Central to this theorem is the notion of the "quality" of a measuring probe; a temperature-dependent strictly positive quantity that serves as a figure of merit of the probe, and that plays the role of $1/\hbar$ in the classical uncertainty relation. This study sets the stage for a new area of research into resource theories of classical measurement, in which high-quality measurements and high-information states of knowledge are the limited resources. |
| title | The limits of knowledge in classical physics resemble the quantum uncertainty relation |
| topic | Statistical Mechanics Classical Physics Quantum Physics |
| url | https://arxiv.org/abs/2503.23698 |