Influence of equilibrium and nonequilibrium environments on macroscopic realism through the Leggett-Garg inequalities

Abstract

We study macroscopic realism through the Leggett-Garg inequalities (LGI) in two interacting qubit system. The two qubits are coupled either with two Bosonic (thermal and photonic) baths or Fermionic (electronic) baths. We study both how the equilibrium and nonequilibrium environments influence the LGI. One way to characterize the nonequilibrium condition is by the different temperatures (for the Bosonic baths) or the different chemical potentials (for the Fermionic baths). We also study the heat or particle current and the entropy production rate generated by the nonequilibrium environments. Analytical forms of the LGI and the maximal values of LGI based on the quantum master equation beyond secular approximation are derived. The LGI function and its maximal value have separated contributions, the part describing the coherent evolution and the part describing the coupling between the system and environments. The environment coupling part can be from equilibrium environment or nonequilibrium environment. The nonequilibrium dynamics is quantified by the Bloch-Redfield equation which is beyond Lindblad form. We found that the nonequilibriumness quantified by the temperature difference or chemical potential difference can lead to the LGI violation or the increase of the maximal value of LGI, restoring the quantum nature from certain equilibrium cases where LGI is preserved which gives rise to classical realism. The corresponding nonequilibrium thermodynamic cost is quantified by the nonzero entropy production rate. The LGI violation enhancement increases with the increase of the entropy production rate under certain nonequilibrium conditions. Therefore, the LGI violation enhancement can be realized by the thermodynamic nonequilibrium cost. Our results shed on light on the nature of the macroscopic realism and the relationship between the nonequilibriumness and quantum temporal correlation. Our finding of nonequilibrium promoted LGI violation suggests a new strategy for the design of quantum information processing and quantum computational devices to maintain the quantum nature and quantum correlations for long.