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 $s^{\prime }=m\left(s\right)$, where $m$ is an involution, $m(m\left(s\right))=s$. 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.

Close

PrevNext

View figure in article

• Fluctuation theorems
• Nonequilibrium & irreversible thermodynamics
• Thermodynamics
• Uncertainty relation