We study the statistics of the work done, the fluctuation relations and the irreversible entropy production in a quantum many-body system subject to the sudden quench of a control parameter. By treating the quench as a thermodynamic transformation we
show that the emergence of irreversibility in the nonequilibrium dynamics of closed many-body quantum systems can be accurately characterized. We demonstrate our ideas by considering a transverse quantum Ising model that is taken out of equilibrium by the instantaneous switching of the transverse field.
A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Losc
hmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here.
Many biological electron transfer (ET) reactions are mediated by metal centres in proteins. NADH:ubiquinone oxidoreductase (complex I) contains an intramolecular chain of seven iron-sulphur (FeS) clusters, one of the longest chains of metal centres i
n biology and a test case for physical models of intramolecular ET. In biology, intramolecular ET is commonly described as a diffusive hopping process, according to the semi-classical theories of Marcus and Hopfield. However, recent studies have raised the possibility that non-trivial quantum mechanical effects play a functioning role in certain biomolecular processes. Here, we extend the semi-classical model for biological ET to incorporate both semi-classical and coherent quantum phenomena using a quantum master equation based on the Holstein Hamiltonian. We test our model on the structurally-defined chain of FeS clusters in complex I. By exploring a wide range of realistic parameters we find that, when the energy profile for ET along the chain is relatively flat, just a small coherent contribution can provide a robust and significant increase in ET rate (above the semi-classical diffusive-hopping rate), even at physiologically-relevant temperatures. Conversely, when the on-site energies vary significantly along the chain the coherent contribution is negligible. For complex I, a crucial respiratory enzyme that is linked to many neuromuscular and degenerative diseases, our results suggest a new contribution towards ensuring that intramolecular ET does not limit the rate of catalysis. For the emerging field of quantum biology, our model is intended as a basis for elucidating the general role of coherent ET in biological ET reactions.
