Condensed Matter Seminar: Entropy Production in Active and Resetting Dynamics: From Effective Temperatures to Thermodynamic Cycles

Run-and-tumble particles and stochastic resetting are two widely studied statistical-mechanical models of nonequilibrium stochastic dynamics. Over the past decade, both have emerged as minimal yet versatile frameworks for exploring irreversibility, steady states, transport, and the energetic costs of nonequilibrium behavior. Despite their conceptual simplicity and broad relevance, the thermodynamic characterization of entropy production in these systems remains incomplete. This talk presents two complementary approaches that connect entropy production in active and resetting dynamics with effective thermodynamic and information-theoretic descriptions.

The first part focuses on run-and-tumble dynamics in both its standard two-state formulation and in models with continuous velocity distributions. Using an inverse-Clausius thermodynamic framework, the dynamics can be mapped onto overdamped Brownian motion in an effective spatially inhomogeneous temperature field reconstructed directly from steady-state observables. Within this approach, local entropy fluxes and entropy production rates can be inferred without explicit knowledge of the full position-velocity distribution. The framework yields a simple thermodynamic interpretation of entropy transfer between hotter- and colder-than-average regions and reveals how the spatial structure of entropy production is linked to the confining potential.

The second part considers stochastic resetting of a Brownian particle confined by an external potential and repeatedly returned to the origin. Interpreting the dynamics as a thermodynamic cycle of spreading and compression leads naturally to a trajectory-level description based on Kullback-Leibler divergences between forward and reversed stochastic dynamics. A coarse-grained formulation depending only on the endpoint distributions provides a state-function-like lower bound for the entropy production. Harmonic confinement emerges as a special case in which the Gaussian propagator structure renders the lower bound theoretically tight, while simulations in anharmonic potentials reveal the same generic qualitative trends.