FieldTheoretic Thermodynamic Uncertainty Relation
Abstract
We propose a fieldtheoretic thermodynamic uncertainty relation as an extension of the one derived so far for a Markovian dynamics on a discrete set of states and for overdamped Langevin equations. We first formulate a framework which describes quantities like current, entropy production and diffusivity in the case of a generic field theory. We will then apply this general setting to the onedimensional KardarParisiZhang equation, a paradigmatic example of a nonlinear fieldtheoretic Langevin equation. In particular, we will treat the dimensionless KardarParisiZhang equation with an effective coupling parameter measuring the strength of the nonlinearity. It will be shown that a fieldtheoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant. The calculations show that the fieldtheoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the KardarParisiZhang equation due to an excess term stemming from its nonlinearity.
 Publication:

Journal of Statistical Physics
 Pub Date:
 January 2020
 DOI:
 10.1007/s1095501902479x
 arXiv:
 arXiv:1908.05560
 Bibcode:
 2020JSP...178.1142N
 Keywords:

 Field theory;
 Nonequilibrium dynamics;
 Thermodynamic uncertainty relation;
 KardarParisiZhang equation;
 Condensed Matter  Statistical Mechanics
 EPrint:
 J Stat Phys 178, 11421174 (2020)