Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 52, Issue 3, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aaf3ff
Keywords
current fluctuations; entropy production; mobility; heat engines; information geometry
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Funding
- World Premier International Research Center Initiative (WPI), MEXT, Japan
- JSPS [17H06460]
- Grants-in-Aid for Scientific Research [17H06460] Funding Source: KAKEN
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We extend a class of recently derived thermodynamic uncertainty relations to vector-valued observables. In contrast to the scalar-valued observables examined previously, this multidimensional thermodynamic uncertainty relation provides a natural way to study currents in high-dimensional systems and to obtain relations between different observables. Our proof is based on the generalized Cramer-Rao inequality, which we interpret as a relation between physical observables and the Fisher information. This allows us to develop high-dimensional versions of both the original, steady state uncertainty relation and the more recently obtained generalized uncertainty relation for time-periodic systems. We apply the multidimensional uncertainty relation to obtain a new constraint on the performance of steady-state heat engines, which is tighter than previous bounds and reveals the role of heat-work correlations. As a second application, we show that the uncertainty relation is connected to a bound on the differential mobility. As a result of this connection, we find that a necessary condition for equality in the uncertainty relation is that the system obeys the equilibrium fluctuation-dissipation relation.
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