4.7 Article

Thermodynamic uncertainty relation from involutions

Journal

PHYSICAL REVIEW E
Volume 106, Issue 6, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.106.L062104

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The thermodynamic uncertainty relation (TUR) is a lower bound for the variance of a current as a function of the average entropy production. Depending on the assumptions, different versions of TUR can be obtained.
The thermodynamic uncertainty relation (TUR) is a lower bound for the variance of a current (over the mean squared) as a function of the average entropy production. Depending on the assumptions, one obtains different versions of the TUR. For instance, from the exchange fluctuation theorem, one obtains a corresponding exchange TUR. Alternatively, we show that TURs are a consequence of a very simple property: Every process s has only one conjugate s' = m(s), where m is an involution, m(m(s)) = s. This property allows the derivation of a general TUR without using any fluctuation theorem. As applications, we obtain the exchange TUR, the hysteretic TUR, a fluctuation-response inequality and a lower bound for the entropy production in terms of other nonequilibrium metrics.

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