Transfer of Entropy between the Magnetic Field and Solar Energetic Particles during an Interplanetary Coronal Mass Ejection

Thermodynamics of solar wind bulk plasma have been routinely measured and quantified, unlike those of solar energetic particles (SEPs), whose thermodynamic properties have remained elusive until recently. The thermodynamic kappa (\(\kappa_{\rm EP}\)) that parameterizes the statistical distribution of SEP kinetic energy contains information regarding the population's level of correlation and effective degrees of freedom (\({\rm d_{eff}}\)). At the same time, the intermittent kappa (\(\kappa_{\Delta B}\)) that parameterizes the statistical distribution of magnetic field increments contains information about the correlation and \({\rm d_{eff}}\) involved in magnetic field fluctuations. Correlations between particles can be affected by magnetic field fluctuations, leading to a relationship between \(\kappa_{\rm EP}\) and \(\kappa_{\Delta B}\). In this paper, we examine the relationship of \({\rm d_{eff}}\) and entropy between energetic particles and the magnetic field via the spatial variation of their corresponding parameter kappa values. We compare directly the values of \(\kappa_{\rm EP}\) and \(\kappa_{\Delta B}\) using Parker Solar Probe IS\(\odot\)IS and FIELDS measurements during an SEP event associated with an interplanetary coronal mass ejection (ICME). Remarkably, we find that \(\kappa_{\rm EP}\) and \(\kappa_{\Delta B}\) are anti-correlated via a linear relationship throughout the passing of the ICME, indicating a proportional exchange of \({\rm d_{eff}}\) from the magnetic field to energetic particles, i.e., \(\kappa_{\Delta B} \sim (-0.15 \pm 0.03)\kappa_{\rm EP}\), interpreted as an effective coupling ratio. This finding is crucial for improving our understanding of ICMEs and suggests that they help to produce an environment that enables the transfer of entropy from the magnetic field to energetic particles due to changes in intermittency of the magnetic field.