| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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Finite temperature Casimir effect of scalar field |
| Liang Chen(陈亮)1,2,3,†, Yu-Jing Wang(王钰婧)1,2, and Sheng-Yan Li(李生艳)1,2 |
1 School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China;
2 Institute of Condensed Matter Physics, North China Electric Power University, Beijing 102206, China;
3 Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China |
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Abstract We derive analytical expressions for the Helmholtz free energy, Casimir force, and Casimir entropy in one- and three-dimensional scalar fields subject to Dirichlet boundary conditions at finite temperature. The problem of negative Casimir entropy is examined in these systems, as well as for a scalar field confined within a three-dimensional (3D) spherical cavity. Our analysis shows that this apparent paradox arises under different regularization schemes involving distinct counterterms. We advocate against introducing any counterterms for the thermal corrections to the Casimir effect and predict that the thermal-fluctuation-induced Casimir force becomes repulsive in the high-temperature limit, specifically when $aT/(\pi\hbar{v})>0.2419$ for the 3D scalar field.
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Received: 03 September 2025
Revised: 14 November 2025
Accepted manuscript online: 27 November 2025
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PACS:
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44.40.+a
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(Thermal radiation)
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62.25.-g
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(Mechanical properties of nanoscale systems)
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65.40.gd
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(Entropy)
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11.10.-z
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(Field theory)
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Corresponding Authors:
Shuyu Lin
E-mail: slchern@ncepu.edu.cn
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Cite this article:
Liang Chen(陈亮), Yu-Jing Wang(王钰婧), and Sheng-Yan Li(李生艳) Finite temperature Casimir effect of scalar field 2026 Chin. Phys. B 35 074401
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