Finite temperature Casimir effect of scalar field

doi:10.1088/1674-1056/ae24ea

中国物理B ›› 2026, Vol. 35 ›› Issue (7): 74401-074401.doi: 10.1088/1674-1056/ae24ea

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

收稿日期:2025-09-03 修回日期:2025-11-14 接受日期:2025-11-27 发布日期:2026-07-15
通讯作者: Shuyu Lin E-mail:slchern@ncepu.edu.cn

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

Received:2025-09-03 Revised:2025-11-14 Accepted:2025-11-27 Published:2026-07-15
Contact: Shuyu Lin E-mail:slchern@ncepu.edu.cn

摘要/Abstract

摘要： 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.

关键词: Casimir effect, Nernst theorem, finite-temperature quantum field theory

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.

Key words: Casimir effect, Nernst theorem, finite-temperature quantum field theory

中图分类号: (Thermal radiation)

44.40.+a

62.25.-g (Mechanical properties of nanoscale systems) 65.40.gd (Entropy) 11.10.-z (Field theory)

Liang Chen(陈亮), Yu-Jing Wang(王钰婧), and Sheng-Yan Li(李生艳). Finite temperature Casimir effect of scalar field[J]. 中国物理B, 2026, 35(7): 74401-074401.

Liang Chen(陈亮), Yu-Jing Wang(王钰婧), and Sheng-Yan Li(李生艳). Finite temperature Casimir effect of scalar field[J]. Chin. Phys. B, 2026, 35(7): 74401-074401.

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Finite temperature Casimir effect of scalar field

Finite temperature Casimir effect of scalar field

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