Regular Article

Thermodynamic uncertainty relations in a linear system

Dipartimento di Fisica ‘G. Galilei’, INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy

^a e-mail: phydeepak.gupta@gmail.com

Received: 8 January 2020
Published online: 12 February 2020

Abstract

We consider a Brownian particle in harmonic confinement of stiffness k, in one dimension in the underdamped regime. The whole setup is immersed in a heat bath at temperature T. The center of harmonic trap is dragged under any arbitrary protocol. The thermodynamic uncertainty relations for both position of the particle and current at time t are obtained using the second law of thermodynamics as well as the positive semi-definite property of the correlation matrix of work and degrees of freedom of the system for both underdamped and overdamped cases.