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Abstract A stationary body that is out of thermal equilibrium with its environment, and for which the electric susceptibility is non-reciprocal, experiences a quantum torque. This arises from the spatially non-symmetric electrical response of the body to its interaction with the non-equilibrium thermal fluctuations of the electromagnetic field: the non-equilibrium nature of the thermal field fluctuations results in a net energy flow through the body, and the spatially non-symmetric nature of the electrical response of the body to its interaction with these field fluctuations causes that energy flow to be transformed into a rotational motion. We establish an exact, closed-form, analytical expression for this torque in the case that the environment is the vacuum and the material of the body is described by a damped oscillator model, where the non-reciprocal nature of the electric susceptibility is induced by an external magnetic field, as for magneto-optical media. We also generalise this expression to the context in which the body is slowly rotating. By exploring the high-temperature expansion of the torque, we are able to identify the separate contributions from the continuous spectral distribution of the non-reciprocal electric susceptibility, and from the resonance modes. In particular, we find that the torque persists in the limiting case of zero damping parameter, due to the contribution of the resonance modes. We also consider the low-temperature expansion of the torque. This work extends our previous consideration of this model to an external magnetic field of arbitrary strength, thereby including non-linear magnetic field effects. 

Gas hydrates (GHs) in water close to freezing temperatures can be stabilised via the formation of ice layers. In a recent work [Boström et al. , Astron. Astrophys. , A54 , 650, 2021], it was found that a surface region with partial gas dilution could be essential for obtaining nano- to micron-sized anomalously stabilizing ice layers. In this paper, it is demonstrated that the Casimir–Lifshitz free energy in multi-layer systems could induce thinner, but more stable, ice layers in cavities than those found for gas hydrates in a large reservoir of cold water. The thickness and stability of such ice layers in a pore filled with cold water could influence the leakage of gas molecules. Additional contributions, e.g. from salt-induced stresses, can also be of importance, and are briefly discussed. 

It has been recognized for some time that, even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self-entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper, we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel–Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.