A satisfactory understanding of macroscopic irreversibility has remained elusive since the advent of thermodynamics. Progress has nevertheless been made in understanding irreversibility measures classically; this work explores irreversibility in a quantum setting. Entropy production quantifies the irreversibility associated with open stochastic dynamical systems, and our main aim has been to extend this concept.

Understanding the thermodynamics of open quantum systems better will eventually improve the efficiency of increasingly feasible nanoscale operations. An exact method to model the thermodynamic properties of open quantum systems is the stochastic Liouville-von Neumann (SLN) equation, based on unravelling Feynman-Vernon influence functionals. We extend its use from the one heat bath case to a system in a non-equilibrium stationary state due to coupling to more than one heat bath.

An asymmetry in the probabilistic specification of a closed deterministic system can lead to a disparity between the likelihoods of a particular forward and corresponding backward behaviour starting from a specified time. Such a comparison is a test of a property denoted obversibility, quantified in terms of dissipation production – rather than entropy production – as a measure of irreversibility. We evaluate dissipation production in a deterministic two-level quantum system described by a statistical ensemble of state vectors. We identify the conditions under which the dissipation production fulfills an Evans-Searles Fluctuation Theorem and for which the system will display time-asymmetric average behaviour as it evolves.

Finally, we use a Kraus operator formalism to present a minimal model for the random evolution in the Bloch sphere of individual trajectory realisations of the coherence vector of a qubit and use it to evaluate the entropy production associated with weak quantum measurement, with both one and two measurement operators, before speculating on the consequences of our results to our understanding of quantum measurement and the associated indeterminism.