32 research outputs found
Additive Property of Drazin Invertibility of Elements
In this article, we investigate additive properties of the Drazin inverse of
elements in rings and algebras over an arbitrary field. Under the weakly
commutative condition of , we show that is Drazin
invertible if and only if is Drazin invertible. Next, we
give explicit representations of , as a function of
and , under the conditions and .Comment: 17 page
Thermodynamic length in open quantum systems
The dissipation generated during a quasistatic 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.
Here, we show how to generalize this approach to open quantum systems by
finding the thermodynamic metric associated to a given Lindblad master
equation. The obtained metric can be understood as a perturbation over the
background geometry of equilibrium Gibbs states, which is induced by the
Kubo-Mori-Bogoliubov (KMB) inner product. We illustrate this construction on
two paradigmatic examples: an Ising chain and a two-level system interacting
with a bosonic bath with different spectral densities.Comment: 22 pages, 3 figures. v5: minor corrections, accepted in Quantu
Work, entropy and uncertainties in thermodynamics beyond the classical and weak coupling regime
Thermodynamics typically concerns the physical behaviour of macroscopic systems comprised of many particles. However, recent theoretical progress has extended the theory to both the classical-stochastic and quantum regimes, where systems are comprised of just a small number of particles. In this thesis I investigate a range of situations in which new thermodynamic phenomena emerge due to the reduced size of the systems involved. One central assumption in macroscopic thermodynamics is the weak coupling approximation, which posits that the equilibrium properties of a system are not influenced by the interactions with its surrounding environment. However, for microscopic systems this assumption can break down, and I derive new fluctuation relations that provide a refined form of the second law of thermodynamics in this strong-coupling regime, taking into account corrections stemming from these interactions. In this work I provide a characterisation of stochastic heat and entropy production for small scale classical systems that are defined regardless of the strength of interaction. I then show that these definitions lead to a consistent thermodynamic framework valid beyond the usual weak-coupling regime. The thesis also concerns the effect of interactions on the equilibrium properties of strongly-coupled quantum systems, and I investigate how these interactions can influence the resulting temperature fluctuations in this regime. Using tools from quantum estimation theory, I derive an uncertainty relation between energy and temperature valid at all coupling strengths and system sizes. The relation reveals how quantum energy coherences contribute to statistical fluctuations in the estimated temperature of small- scale systems. Finally, I investigate how quantum fluctuations influence the statistics of work extracted from slowly-driven quantum systems. I prove that, unlike in classical systems, the work dissipated by a general quantum system is no longer proportional to its statistical fluctuations. This result reveals new subtleties involved in designing optimal quantum thermodynamic processes