423 research outputs found
Thermodynamic work from operational principles
In recent years we have witnessed a concentrated effort to make sense of
thermodynamics for small-scale systems. One of the main difficulties is to
capture a suitable notion of work that models realistically the purpose of
quantum machines, in an analogous way to the role played, for macroscopic
machines, by the energy stored in the idealisation of a lifted weight. Despite
of several attempts to resolve this issue by putting forward specific models,
these are far from capturing realistically the transitions that a quantum
machine is expected to perform. In this work, we adopt a novel strategy by
considering arbitrary kinds of systems that one can attach to a quantum thermal
machine and seeking for work quantifiers. These are functions that measure the
value of a transition and generalise the concept of work beyond the model of a
lifted weight. We do so by imposing simple operational axioms that any
reasonable work quantifier must fulfil and by deriving from them stringent
mathematical condition with a clear physical interpretation. Our approach
allows us to derive much of the structure of the theory of thermodynamics
without taking as a primitive the definition of work. We can derive, for any
work quantifier, a quantitative second law in the sense of bounding the work
that can be performed using some non-equilibrium resource by the work that is
needed to create it. We also discuss in detail the role of reversibility and
correlations in connection with the second law. Furthermore, we recover the
usual identification of work with energy in degrees of freedom with vanishing
entropy as a particular case of our formalism. Our mathematical results can be
formulated abstractly and are general enough to carry over to other resource
theories than quantum thermodynamics.Comment: 22 pages, 4 figures, axioms significantly simplified, more
comprehensive discussion of relationship to previous approache
Statistical ensembles without typicality
Maximum-entropy ensembles are key primitives in statistical mechanics from
which thermodynamic properties can be derived. Over the decades, several
approaches have been put forward in order to justify from minimal assumptions
the use of these ensembles in statistical descriptions. However, there is still
no full consensus on the precise reasoning justifying the use of such
ensembles. In this work, we provide a new approach to derive maximum-entropy
ensembles taking a strictly operational perspective. We investigate the set of
possible transitions that a system can undergo together with an environment,
when one only has partial information about both the system and its
environment. The set of all these allowed transitions encodes thermodynamic
laws and limitations on thermodynamic tasks as particular cases. Our main
result is that the set of allowed transitions coincides with the one possible
if both system and environment were assigned the maximum entropy state
compatible with the partial information. This justifies the overwhelming
success of such ensembles and provides a derivation without relying on
considerations of typicality or information-theoretic measures.Comment: 9+9 pages, 3 figure
Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
It is well known that if a (finite-dimensional) density matrix ρ has smaller entropy than ρ0, then the tensor product of sufficiently many copies of ρ majorizes a quantum state arbitrarily close to the tensor product of correspondingly many copies of ρ0. In this short note I show that if additionally rank(ρ) ≤ rank(ρ0), then n copies of ρ also majorize a state where all single-body marginals are exactly identical to ρ0 but arbitrary correlations are allowed (for some sufficiently large n). An immediate application of this is an affirmative solution of the exact catalytic entropy conjecture introduced by Boes et al. [PRL 122, 210402 (2019)]: If H(ρ) < H(ρ0) and rank(ρ) ≤ rank(ρ0) there exists a finite dimensional density matrix σ and a unitary U such that Uρ⊗ σU has marginals ρ0 and σ exactly. All the results transfer to the classical setting of probability distributions over finite alphabets with unitaries replaced by permutations
Single-shot holographic compression from the area law
The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. We show that, for any state that fulfills an area law, the reduced quantum state of a region of space can be unitarily compressed into a thickened boundary of the region. If the interior of the region is lost after this compression, the full quantum state can be recovered to high precision by a quantum channel only acting on the thickened boundary. The thickness of the boundary scales inversely proportional to the error for arbitrary spin systems and logarithmically with the error for quasifree bosonic systems. Our results can be interpreted as a single-shot operational interpretation of the area law. The result for spin systems follows from a simple inequality showing that any probability distribution with entropy S can be approximated to error ϵ by a distribution with support of size exp(S/ϵ), which we believe to be of independent interest. We also discuss an emergent approximate correspondence between bulk and boundary operators and the relation of our results to tensor network states
Work and entropy production in generalised Gibbs ensembles
Recent years have seen an enormously revived interest in the study of
thermodynamic notions in the quantum regime. This applies both to the study of
notions of work extraction in thermal machines in the quantum regime, as well
as to questions of equilibration and thermalisation of interacting quantum
many-body systems as such. In this work we bring together these two lines of
research by studying work extraction in a closed system that undergoes a
sequence of quenches and equilibration steps concomitant with free evolutions.
In this way, we incorporate an important insight from the study of the dynamics
of quantum many body systems: the evolution of closed systems is expected to be
well described, for relevant observables and most times, by a suitable
equilibrium state. We will consider three kinds of equilibration, namely to (i)
the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised
Gibbs ensemble (GGE), reflecting further constants of motion in integrable
models. For each effective description, we investigate notions of entropy
production, the validity of the minimal work principle and properties of
optimal work extraction protocols. While we keep the discussion general, much
room is dedicated to the discussion of paradigmatic non-interacting fermionic
quantum many-body systems, for which we identify significant differences with
respect to the role of the minimal work principle. Our work not only has
implications for experiments with cold atoms, but also can be viewed as
suggesting a mindset for quantum thermodynamics where the role of the external
heat baths is instead played by the system itself, with its internal degrees of
freedom bringing coarse-grained observables to equilibrium.Comment: 22 pages, 4 figures, improvements in presentatio
- …