Uncertainty relations in stochastic processes: An information inequality approach

Understand

The thermodynamic uncertainty relation is an inequality stating that it is impossible to attain higher precision than the bound defined by entropy production.

• In statistical inference theory, information inequalities assert that it is infeasible for any estimator to achieve an error smaller than the prescribed bound.
• Inspired by the similarity between the thermodynamic uncertainty relation and the information inequalities, we apply the latter to systems described by Langevin equations and derive the bound for the fluctuation of thermodynamic quantities.
• When applying the Cram\'er-Rao inequality, the obtained inequality reduces to the fluctuation-response inequality.