One loop field theory calculations of free energies quite often yield violations of the stability conditions associated with the thermodynamic second law. Perhaps the best known example involves the equation of state of black holes. Here, it is pointed out that the Casimir force between two parallel conducting plates also violates a thermodynamic stability condition normally associated with the second law of thermodynamics.
We review recent results on the low-temperature behaviors of the Casimir-Polder and Casimir free energy an entropy for a polarizable atom interacting with a graphene sheet and for two graphene sheets, respectively. These results are discussed in the wide context of problems arising in the Lifshitz theory of van der Waals and Casimir forces when it is applied to metallic and dielectric bodies. After a brief treatment of different approaches to theoretical description of the electromagnetic response of graphene, we concentrate on the derivation of response function in the framework of thermal qu…
We consider Casimir-Polder and Casimir forces with finite dissipation by coupling heat baths to the dipoles introducing, this way, dissipation from 'first principles'. We derive a representation of the free energy as an integral over real frequencies, which can be viewd as an generalization of the 'remarkable formula' introduced by Ford et. al. 1985. For instance, we obtain a nonperturbative representation for the atom-atom and atom-wall interactions. We investigate several limiting cases. From the limit $T\to0$ we show that the third law of thermodynamics cannot be violated within the given a…
The analytic asymptotic expressions for the Casimir free energy and entropy for two parallel graphene sheets possessing nonzero energy gap $Δ$ and chemical potential $μ$ are derived at arbitrarily low temperature. Graphene is described in the framework of thermal quantum field theory in the Matsubara formulation by means of the polarization tensor in (2+1)-dimensional space-time. Different asymptotic expressions are found under the conditions $Δ>2μ$, $Δ=2μ$, and $Δ<2μ$ taking into account both the implicit temperature dependence due to a summation over the Matsubara frequencies and the explici…
Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
Thermal Casimir Effect in A Schwarzschild-like Wormhole Spacetime
Sepuluh Nopember Institute of Technology（十十一月理工大学）；Universitas Islam Negeri Maulana Malik Ibrahim Malang（穆拉纳马利克伊布拉欣伊斯兰国立大学）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；National Research and Innovation Agency (BRIN)（国家研究与创新署）；Universitas Indonesia（印度尼西亚大学）
On the Temperature Dependence of the Casimir Effect
根据金、铜等金属色散关系的光学数据，分析了实际金属平板与金属球之间Casimir力的温度关系。现实的双折射率意味着，连同基本的热力学考虑，横向电零模式没有贡献。这导致了与传统预测的可观察差异，传统预测没有考虑到这种物理要求。结果表明，与热力学第三定律是一致的，以及与当前的实验是一致的。然而，预测的温度依赖性应该在未来的实验中检测到。基于{ \it ad hoc}假设的方法的不足之处，如等离子体色散关系和使用的表面阻抗没有横向动量的依赖，进行了讨论。
It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model for a damped oscillator is suggested along the lines of the general theory of Casimir and van der Waals forces, and the corresponding thermodynamic quantities obtained. While the original model involves a heat bath consisting of a large number of free oscillators having infinitesimal damping functions, the extended model allows any generally admissible freq…
The particles produced from the vacuum in the dynamical Casimir effect are highly entangled. In order to quantify the correlations generated by the process of vacuum decay induced by moving mirrors, we study the entanglement evolution in the dynamical Casimir effect by computing the time-dependent Rényi and von Neumann entanglement entropy analytically in arbitrary dimensions. We consider the system at parametric resonance, where the effect is enhanced. We find that, in (1+1) dimensions, the entropies grow logarithmically for large times, $S_A(τ)\sim\frac{1}{2}\log(τ)$, while in higher dimensi…
In the present paper we investigate thermal fluctuation corrections to the vacuum energy at zero temperature of a conformally coupled massless scalar field whose modes propagate in the Einstein universe with a spherical boundary, characterized by both Dirichlet and Neumann boundary conditions. Thus, we generalize the results found in literature in this scenario, which has considered only the vacuum energy at zero temperature. To do this, we use the generalized zeta function method plus Abel-Plana formula and calculate the renormalized Casimir free energy as well as other thermodynamics quantit…
In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for …
