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Stochastic thermodynamics of relativistic Brownian motion

Physical scenarios that require a relativistic treatment are ubiquitous in nature, ranging from cosmological objects to charge carriers in Dirac materials. Interestingly all of these situations have in common that the systems typically operate very far from thermal equilibrium. Therefore, if and how the framework of stochastic thermodynamics applies at relativistic energies is a salient question. In the present work we generalize the notions of stochastic heat and work for the relativistic Langevin equation and derive the fluctuation theorems without and with feedback. For processes with feedback we consider the ramifications of the lack of simultaneity of events in the inertial frames of observer and Brownian particles, and we argue that the framework of absolute irreversibility is instrumental to avoid acausal considerations. The analysis is concluded with a few remarks on potential experimental applications in graphene.