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Tightening the uncertainty principle for the currents | M. Polettini
; A. Lazarescu
; M. Esposito
; | Date: |
31 May 2016 | Abstract: | We connect two recent advances in the stochastic analysis of nonequilibrium
systems: the (loose) uncertainty principle for the currents, which states that
statistical errors are bounded by thermodynamic dissipation; and the analysis
of thermodynamic consistency of the currents in the light of symmetries.
Employing the large deviation techniques exposed in [Gingrich et al., Phys.
Rev. Lett. 2016] and [Pietzonka et al., arXiv:1512.01221], we prove a tighter
uncertainty relation for a class of thermodynamically consistent currents $J$.
Our bound involves a measure of partial entropy production, that we interpret
as the least amount of entropy that a system sustaining current $J$ can
possibly produce, at a given steady state. Thermodynamic consistency properly
keeps into account the steady-state constraint $
abla jmath = 0$. We provide
a complete mathematical understanding of quadratic bounds that perform better
than the loose bound, and finally we argue that the relationship for the Fano
factor of the entropy production rate $mathrm{var}, sigma / mathrm{mean},
sigma geq 2$ is the most significant realization of the loose bound. Our
analysis is mainly based on the formalism of diffusions, with an incursion into
Markovian jump processes in the light of the theory of cycle observables. | Source: | arXiv, 1605.9692 | Services: | Forum | Review | PDF | Favorites |
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