Information bound for entropy production from the detailed fluctuation theorem

Fluctuation theorems impose fundamental bounds in the statistics of entropy production with second law thermodynamics being most famous. Using information theory, we quantify and find an upper tight bound as a function its mean from strong detailed fluctuation theorem. The is given terms maximal distribution, member exponential family nonlinear argument. We show that produced by heat transfer using bosonic mode at weak coupling reproduces distribution limiting case. extended to continuous domain verified for levitated nanoparticle. Finally, composition qubit swap engines satisfies particular case regardless size.