Stochastic thermodynamics and fluctuations in heat released by magnetic nanoparticles in response to time-varying fields

Time-varying external magnetic fields can be used to manipulate the dynamics of magnetic nanoparticles. When suspended in viscous media, external fields not only modify the internal N\'eel relaxation dynamics within the magnetic nanoparticles but also the Brownian particle rotation. For the case of oscillating magnetic fields, Brownian and N\'eel processes lead to magnetic losses that are dissipated as heat to the neighborhood of the nanoparticle. The mean value of heat dissipated has been studied intensively in recent years, not least because of promising biomedical applications such as magnetic fluid hyperthermia. Here, we use the framework of stochastic thermodynamics to study fluctuations in the dissipated heat. We find that the dynamics of magnetic nanoparticles as modelled by a mesoscopic model obeys the detailed fluctuation theorem in terms of the total entropy production within numerical accuracy. In addition, we observe that the total entropy production is dominated by the dissipated heat and that fluctuations of dissipated heat are rather strong with the standard deviation being of the same order as the mean value. We also find that the probability of observing negative values of dissipated heat is rather large for typical field strengths used in magnetic fluid hyperthermia applications.