On A Local Carnot Engine

TL;DR

This paper analytically investigates a nonequilibrium quantum system coupled to two heat baths at different temperatures, deriving evolution equations for density and temperature gradients, revealing unique spectral properties depending on temperature profiles.

Contribution

It introduces a novel bilinear coupling between density and temperature gradient in a quantum lattice gas model, extending the understanding of local Carnot engine dynamics.

Findings

Stationary solutions and relaxation times are derived for different temperature couplings.

Discrete and continuous spectra are found depending on temperature profile shapes.

A new evolution equation with bilinear coupling contrasts conventional linear models.

Abstract

Starting from a master equation in a quantum Hamilton form we study analytically a nonequilibrium system which is coupled locally to two heat bathes at different temperatures. Based on a lattice gas description an evolution equation for the averaged density in the presence of a temperature gradient is derived. Firstly, the case is analysed where a particle is removed from a heat bath at a fixed temperature and is traced back to the bath at another temperature. The stationary solution and the relaxation time is discussed. Secondly, a collective hopping process between different heat bathes is studied leading to an evolution equation which offers a bilinear coupling between density and temperature gradient contrary to the conventional approach. Whereas in case of a linear decreasing static temperature field the relaxtion time offers a continuous spectrum it results a discrete spectrum for a quadratically decreasing temperature profile.