Network analysis for the steady-state thermodynamic uncertainty relation

Yasuhiro Utsumi

doi:10.1103/physreve.110.044103

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arXiv · 2405.03611

Network analysis for the steady-state thermodynamic uncertainty relation

Yasuhiro Utsumi

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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.

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BibTeX RIS

Yasuhiro Utsumi. 2024-05-06. Network analysis for the steady-state thermodynamic uncertainty relation. https://doi.org/10.1103/physreve.110.044103

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