The average dissipation generated during a slow thermodynamic process can be characterised by introducing a metric on the space of Gibbs states, in such a way that minimally-dissipating protocols correspond to geodesic trajectories. Furthermore, the dissipation is proportional to the work fluctuations for classical systems (which follows from the fluctuation-dissipation relation (FDR)), so that minimising dissipation also minimises fluctuations. In this talk, I will explain how this geometric picture is modified in the quantum regime.
The field of quantum information takes a pragmatic approach to examining and utilizing quantum mechanics, seeking to obtain rigorous understandings of which information processing tasks can (e.g. quantum computing, communication) or cannot (e.g.
Systems with time-dependent Hamiltonians are not constrained to energy conservation. Hence, the dynamics of driven physical systems can be significantly different to its static counterpart. Then, driven systems are a new platform where exciting phenomena can be discovered. However, analytical solutions of the dynamics of driven systems are extremely rare and it is typically difficult to gain intuition.
We investigate the fundamental trade-off between current fluctuations and entropy production for systems in non-equilibrium steady states (NESS). We use the technique of non-equilibrium statistical operators of McLennan/Zubarev form and illustrate how the entropy production can be expressed as a quantum relative entropy. Furthermore, by exploiting the geometry of the manifold of NESS states, we use parameter estimation in order to bound the co-variance of the currents in the NESS by the entropy production.