Related papers: The Second Law of Quantum Complexity
The Boltzmann-Gibbs-von Neumann entropy of a large part (of linear size L) of some (much larger) d-dimensional quantum systems follows the so-called area law (as for black holes), i.e., it is proportional to $L^{d-1}$. Here we show, for…
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We develop both…
The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory…
Quantum buoyancy has been proposed as the mechanism protecting the generalized second law when an entropy--bearing object is slowly lowered towards a black hole and then dropped in. We point out that the original derivation of the buoyant…
To explain black hole thermodynamics in quantum gravity, one must introduce constraints to ensure that a black hole is actually present. I show that for a large class of black holes, such ``horizon constraints'' allow the use of conformal…
To derive black hole thermodynamics in any quantum theory of gravity, one must introduce constraints that ensure that a black hole is actually present. For a large class of black holes, the imposition of such ``horizon constraints'' allows…
The second law of thermodynamics is the cornerstone of physics, characterizing the convertibility between thermodynamic states through a single function, entropy. Given the universal applicability of thermodynamics, a fundamental question…
Hermiticity is usually treated as a foundational axiom of quantum mechanics, guaranteeing real spectra and unitary time evolution. In this work we argue that Hermiticity is more naturally understood as a symmetry law arising from the global…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
I review various proposals for the nature of black hole entropy and for the mechanism behind the operation of the generalized second law. I stress the merits of entanglement entropy {\tenit qua\/} black hole entropy, and point out that,…
Black hole thermodynamics suggests that a black hole should have an entropy given by a quarter of the area of its horizon. Earlier calculations in U(1) loop quantum gravity have led to a dominant term proportional to the area, but there was…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…
I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underly the thermodynamics of other systems. (Here…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a…
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in…
Earlier calculations of black hole entropy in loop quantum gravity have given a term proportional to the area with a correction involving the logarithm of the area when the area eigenvalue is close to the classical area. However the…
Adopting the thin-layer improved brick-wall method, we investigate the thermodynamics of a black hole embedded in a spatially flat Friedmann-Robertson-Walker universe. We calculate the temperature and the entropy at every apparent horizon…
Within the framework of the "complexity equals action" and "complexity equals volume" conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes…