A thermodynamic uncertainty relation for a system with memory

Abstract

We introduce an example of thermodynamic uncertainty relation (TUR) for systems modeled by a one-dimensional generalised Langevin dynamics with memory, determining the motion of a micro-bead driven in a complex fluid. Contrary to TURs typically discussed in the previous years, our observables and the entropy production rate are one-time variables. The bound to the signal-to-noise ratio of such state-dependent observables only in some cases can be mapped to the entropy production rate. For example, this is true in Markovian systems. Hence, the presence of memory in the system complicates the thermodynamic interpretation of the uncertainty relation.

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• Energetics of critical oscillators in active bacterial baths
• Variance sum rule: proofs and solvable models
• Heat production in a stochastic system with nonlinear time-delayed feedback
• Force-free kinetic inference of entropy production
• The Two Scaling Regimes of the Thermodynamic Uncertainty Relation for the KPZ-Equation