Non-equilibrium reversible dynamics of work production in four-spin system in a magnetic field

TL;DR

This paper derives and analyzes a set of equations describing the reversible, non-equilibrium dynamics of work production in a four-spin system under a time-dependent magnetic field, combining analytical and numerical methods.

Contribution

It introduces a closed-form set of equations for local Bloch vectors and correlations in a four-spin system, enabling detailed analysis of quantum thermodynamics under external magnetic fields.

Findings

Reversible work production dynamics depend on initial states and magnetic field modulation.

Analytical solutions are obtained for specific initial conditions.

Numerical simulations confirm the theoretical predictions.

Abstract

A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for 4 magnetic particles with the exchange interaction that takes place in an arbitrary time-dependent external magnetic field. The analytical and numerical analysis of the quantum thermodynamic variables is carried out depending on separable mixed initial state and the magnetic field modulation. Under unitary evolution, non-equilibrium reversible dynamics of power production in the finite environment is investigated.