Network analysis for the steady-state thermodynamic uncertainty relation

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.

arXiv comment10 pages, 2 figures (+Supplemental Material: 4 pages, 1 figure)

References in corpus (17)

• Dissipation bounds all steady-state current fluctuations
• Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
• Fluctuation theorem for currents and Schnakenberg network theory
• Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Inferring dissipation from current fluctuations
• Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
• Fundamental Bounds on First Passage Time Fluctuations for Currents
• Tightening the uncertainty principle for stochastic currents
• A formal view on 2.5 large deviations and fluctuation relations
• Bounds on current fluctuations in periodically driven systems
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Affinity- and topology-dependent bound on current fluctuations
• Thermodynamic uncertainty relation for first-passage times on Markov chains
• Uncertainty relations and fluctuation theorems for Bayes nets
• Full Counting Statistics for Number of Electrons Dwelling in a Quantum Dot
• Thermodynamic cost of Brownian computers in the stochastic thermodynamics of resetting