Inverse Clausius Thermodynamics in Run-and-Tumble Dynamics

Abstract: We consider a one-dimensional run-and-tumble particle (RTP) confined by an external potential and coupled to a thermal reservoir. Starting from the corresponding Fokker-Planck equation, we derive an explicit expression for the local entropy flux between the system and the heat bath. We then construct a thermodynamic representation of the RTP dynamics, modeling the system as an overdamped particle in a medium with a spatially inhomogeneous effective temperature field, determined directly from the entropy flux. This forms the basis of an Inverse Clausius Thermodynamics framework, in which thermodynamic quantities are inferred from entropy exchange with the heat bath rather than postulated. In addition to an exact expression for the entropy flux, the framework introduces a physically motivated approximation for evaluating the local entropy production rate. The approach is computationally efficient and broadly applicable, and is particularly well suited for RTP models where propulsion velocities are redrawn from a continuous distribution at each tumbling event rather than restricted to discrete states.