Stochastic process behind nonlinear thermodynamic quantum master equation

TL;DR

This paper introduces a stochastic process model in Hilbert space that reproduces the nonlinear thermodynamic quantum master equation, linking stochastic dynamics with quantum thermodynamics.

Contribution

It presents a novel piecewise deterministic Markovian jump process that captures the nonlinear thermodynamic quantum master equation with a simple, average normalization property.

Findings

The stochastic process reproduces the thermodynamic quantum master equation.

Identifies detailed balance and fluctuation-dissipation relations for the process.

Connects stochastic trajectories with density matrix evolution.

Abstract

We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple because the normalization of the vectors in Hilbert space is preserved only on average. As a consequence of the nonlinearity of the thermodynamic master equation, the construction of stochastic trajectories involves the density matrix as a running ensemble average. We identify a principle of detailed balance and a fluctuation-dissipation relation for our Markovian jump process.