The smallest absorption refrigerator: the thermodynamics of a system with quantum local detailed balance

We study the thermodynamics of a quantum system interacting with different baths in the repeated interaction framework. In an appropriate limit, the evolution takes the Lindblad form and the corresponding thermodynamic quantities are determined by the state of the full system plus baths. We identify conditions under which the thermodynamics of the open system can be described only by system properties and find a quantum local detailed balance condition with respect to an equilibrium state that may not be a Gibbs state. The three-qubit refrigerator introduced in [N. Linden, S. Popescu and P. Skrzypczyk, Phys. Rev. Lett.${\bf 105}$, 130401 (2010)] is an example of such a system. From a repeated interaction microscopic model we derive the Lindblad equation that describes its dynamics and discuss its thermodynamic properties for arbitrary values of the internal coupling between the qubits. We find that external power (proportional to the internal coupling strength) is required to bring the system to its steady state, but once there, it works autonomously as discussed in [N. Linden, S. Popescu and P. Skrzypczyk, Phys. Rev. Lett. ${\bf 105}$, 130401 (2010)].Comment: 11 pages, 2 figure

Realization of minimal C*-dynamical systems in terms of Cuntz-Pimsner algebras

In the present paper we study tensor C*-categories with non-simple unit realised as C*-dynamical systems (F,G,\beta) with a compact (non-Abelian) group G and fixed point algebra A := F^G. We consider C*-dynamical systems with minimal relative commutant of A in F, i.e. A' \cap F = Z, where Z is the center of A which we assume to be nontrivial. We give first several constructions of minimal C*-dynamical systems in terms of a single Cuntz-Pimsner algebra associated to a suitable Z-bimodule. These examples are labelled by the action of a discrete Abelian group (which we call the chain group) on Z and by the choice of a suitable class of finite dimensional representations of G. Second, we present a construction of a minimal C*-dynamical system with nontrivial Z that also encodes the representation category of G. In this case the C*-algebra F is generated by a family of Cuntz-Pimsner algebras, where the product of the elements in different algebras is twisted by the chain group action. We apply these constructions to the group G = SU(N).Comment: 34 pages; References updated and typos corrected. To appear in International Journal of Mathematic

Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center

In the present paper we prove a duality theory for compact groups in the case when the C*-algebra A, the fixed point algebra of the corresponding Hilbert C*-system (F,G), has a nontrivial center Z and the relative commutant satisfies the minimality condition A.'\cap F = Z as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*-categories T_\c < T, where T_\c{i}s a suitable DR-category and T a full subcategory of the category of endomorphisms of A. Both categories have the same objects and the arrows of T can be generated from the arrows of T_\c{a}nd the center Z. A crucial new element that appears in the present analysis is an abelian group C(G), which we call the chain group of G, and that can be constructed from certain equivalence relation defined on G^, the dual object of G. The chain group, which is isomorphic to the character group of the center of G, determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(G) encodes the possibility of defining a symmetry $\epsilon$ also for the larger category T of the previous inclusion.Comment: Final version appeared in Int. J. Math. 15 (2004) 759-812. Minor changes w.r.t. to the previous versio

Stochastic thermodynamics of quantum maps with and without equilibrium

We study stochastic thermodynamics for a quantum system of interest whose dynamics are described by a completely positive trace-preserving (CPTP) map as a result of its interaction with a thermal bath. We define CPTP maps with equilibrium as CPTP maps with an invariant state such that the entropy production due to the action of the map on the invariant state vanishes. Thermal maps are a subgroup of CPTP maps with equilibrium. In general, for CPTP maps, the thermodynamic quantities, such as the entropy production or work performed on the system, depend on the combined state of the system plus its environment. We show that these quantities can be written in terms of system properties for maps with equilibrium. The relations that we obtain are valid for arbitrary coupling strengths between the system and the thermal bath. The fluctuations of thermodynamic quantities are considered in the framework of a two-point measurement scheme. We derive the entropy production fluctuation theorem for general maps and a fluctuation relation for the stochastic work on a system that starts in the Gibbs state. Some simplifications for the probability distributions in the case of maps with equilibrium are presented. We illustrate our results by considering spin 1/2 systems under thermal maps, non-thermal maps with equilibrium, maps with non-equilibrium steady states and concatenations of them. Finally, we consider a particular limit in which the concatenation of maps generates a continuous time evolution in Lindblad form for the system of interest, and we show that the concept of maps with and without equilibrium translates into Lindblad equations with and without quantum detailed balance, respectively. The consequences for the thermodynamic quantities in this limit are discussed.Comment: 17 pages, 4 figures; new section added, typos correcte

Fifteen-year experiences of the internationally shared aquifer resources management initiative (ISARM) of UNESCO at the global scale

Study region: Global scale. Study focus: This paper highlights the main outputs and outcomes of the Internationally Shared Aquifer Resources Management Initiative (ISARM, 2000–2015) of UNESCO on the global scale. We discuss the lessons learned, what is still relevant in ISARM, and what we consider irrelevant and why. We follow with discussion on the looming scenarios and the next steps following the awareness on transboundary aquifers (TBAs) as identified by ISARM. New insights for the region: This analysis emphasizes the need for more scientific data, widespread education and training, and a more clearly defined role for governments to manage groundwater at the international level. It describes the links, approach and relevance of studies on TBAs to the UN Law of Transboundary Aquifers and on how they might fit regional strategies to assess and manage TBAs. The study discusses an important lesson learned on whether groundwater science can solve transboundary issues alone. It has become clear that science should interact with policy makers and social entities to have meaningful impacts on TBAs. Bringing together science, society, law, policy making, and harmonising information, would be important drivers and the best guidance for further assessments. ISARM can still make contributions, but it could be redesigned to support resolving TBAs issues which, in addition to science (hydrogeology), require considering social, political, economic and environmental factors. ISARM can increase its international dimension in the continents that still lag behind the assessment and shared management of TBAs, such as Asia and Africa.Peer ReviewedPostprint (published version

Amenability and paradoxicality in semigroups and C*-algebras

We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also F{\o}lner's type characterizations of amenability and give an example of a semigroup whose semigroup ring is algebraically amenable but has no F{\o}lner sequence. In the context of inverse semigroups $S$ we give a characterization of invariant measures on $S$ (in the sense of Day) in terms of two notions: $domain$ $measurability$ and $localization$. Given a unital representation of $S$ in terms of partial bijections on some set $X$ we define a natural generalization of the uniform Roe algebra of a group, which we denote by $\mathcal{R}_X$. We show that the following notions are then equivalent: (1) $X$ is domain measurable; (2) $X$ is not paradoxical; (3) $X$ satisfies the domain F{\o}lner condition; (4) there is an algebraically amenable dense *-subalgebra of $\mathcal{R}_X$; (5) $\mathcal{R}_X$ has an amenable trace; (6) $\mathcal{R}_X$ is not properly infinite and (7) $[0]\not=[1]$ in the $K_0$-group of $\mathcal{R}_X$. We also show that any tracial state on $\mathcal{R}_X$ is amenable. Moreover, taking into account the localization condition, we give several C*-algebraic characterizations of the amenability of $X$. Finally, we show that for a certain class of inverse semigroups, the quasidiagonality of $C_r^*\left(X\right)$ implies the amenability of $X$. The converse implication is false.Comment: 29 pages, minor corrections. Mistake in the statement of Proposition 4.19 from previous version corrected. Final version to appear in Journal of Functional Analysi

Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal

We investigate the critical behavior of the open coherently-driven Bose-Hubbard dimer under nonlocal dissipation. A conserved quantity arises from the nonlocal nature of the dissipation, rendering the dimer multistable. In the weak-coupling semiclassical limit, the displayed criticality takes the form of amplitude bistability and breaking of spatial and temporal symmetries. A period-bistable time crystal is formed, consisting of Josephson-like oscillations. Mean-field dynamics and quantum trajectories complement the spectral analysis of the Liouvillian in the approach to the semiclassical limit.Comment: Accepted in PRB. 6 pages, 2 figures. Supplemental material included. Comments are welcom

Hydrological conceptual model characterisation of an abandoned mine site in semiarid climate : the Sierra de Cartagena-La Unión (SE Spain)

A comprehensive study at Sierra de Cartagena-La Unión (SE Spain) abandoned mine site was carried out to characterise the regime and water quality of the groundwater system after the mine closure. The system consists of five geologic fractured blocks belonging to the Alpujarride and Nevado-Filabride complexes. The aquifer units are composed of limestone and dolostone materials. Recharge is mainly controlled by the N-130 fault system, man-made induced fractures, open-pits and underground workings. Discharge is indicated from open pit lakes by the proximal dome-shaped groundwater level contours. Aquifer natural recharge, assessed by fracture density maps and chloride mass balance, provided consistent results. The water hydrochemical facies show a marked sulphate concentration and acidic pH (average pH of 2.53-6.30). A maximum concentration of 4,100 mg/L of Zn and 40,000 mg/L of sulphate was observed in open-pit lakes. Springs present the lowest residence time and are low mineralised with an average pH of 7.6. Geochemical modelling based on the PHREEQCI code indicates water undersaturation with respect to almost all related mineral species and anoxic conditions prevail in the system. Although an adequate understanding of the regional system is provided, a further detailed hydrochemical study is necessary to assess the undergoing geochemical changes