Network analysis for the steady-state thermodynamic uncertainty relation

TL;DR

This paper introduces a network-based method to estimate a lower bound on steady-state current noise in non-equilibrium systems, linking graph theory with thermodynamic uncertainty relations to account for fluctuations and logical irreversibility.

Contribution

It derives a novel noise lower bound using graph theory and large deviation functions, explicitly capturing the effects of logical irreversibility in steady-state systems.

Findings

Derived a noise lower bound based on mesh currents and graph theory.

Applied the bound to a Brownian computation model with reset, showing dependence on system irreversibility.

Bound differs from existing entropy-based bounds by considering extraneous predecessors.

Abstract

We perform network analysis of a system described by the master equation to estimate the lower bound of the steady-state current noise, starting from the level 2.5 large deviation function and using the graph theory approach. When the transition rates are uniform, and the system is driven to a non-equilibrium steady state by unidirectional transitions, we derive a noise lower bound, which accounts for fluctuations of sojourn times at all states and is expressed using mesh currents. This bound is applied to the uncertainty in the signal-to-noise ratio of the fluctuating computation time of a schematic Brownian computation plus reset process described by a graph containing one cycle. Unlike the mixed and pseudo-entropy bounds that increase logarithmically with the length of the intended computation path, this bound depends on the number of extraneous predecessors and thus captures the logical irreversibility.