Resetting entropy production in continuum sluggish dynamics

Determine the resetting entropy production for sluggish dynamics in the continuum, including a regularised or coarse-grained treatment of the resetting-point entropy necessitated by the singular effective potential at the origin and the vanishing stationary density at the reset point.

Background

The paper studies sluggish random walks whose position-dependent diffusivity decreases away from the origin, coupled to Poissonian or threshold resetting. For Poissonian resetting, the continuum stationary density vanishes at the reset point when the sluggishness parameter is positive because the diffusivity is singular there. Consequently, the resetting entropy production defined through the logarithmic ratio of the stationary density at the pre-reset position and at the reset point diverges in the continuum, whereas the corresponding lattice model has a finite entropy production.

The unresolved issue is how to define and evaluate resetting entropy production consistently in the continuum despite this singularity. A regularised or coarse-grained description may be required to assign a finite or otherwise physically interpretable resetting-point entropy and to connect the continuum result with the finite lattice behavior.