Year: 2026
Type: preprint
Abstract: Bounds on entropy production convert limited observations into constraints on hidden dissipation. The Jensen bound expresses a lower bound on the total and subsystem entropy production rates of continuous stochastic systems in terms of mean coordinate rates alone. We show that the same convexity structure yields a complementary upper bound, inspired by Mercer's reflection inequality. For the quadratic entropy-production functional of overdamped Langevin dynamics, Mercer's reflection inequality is identical to the sharp Bhatia-Davis variance bound and coincides with the convex dual of the smallest affine majorant of the functional over the range of the local current. The two bounds yield a two-sided sandwich controlled solely by the mean drift and the extrema of the current, organized into a hierarchy of optimal bounds in which each further observation tightens the ceiling. The thermodynamic uncertainty relation supplies an independent fluctuation floor. We also treat position-dependent diffusion, underdamped dynamics and the tilted periodic potential, for which the weak-barrier series is obtained in closed form and the strong-barrier regime is solved asymptotically. We check the bounds numerically on the Brownian motor.
Source: arXiv (Cornell University)
Authors: Guo, Xiao-Kan, Huang, Zhiqiang
Institutions: Yancheng Institute of Technology, Hubei University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G3810660562, G6835475518
OpenAlex ID: W7223980526