Related papers: The Second Law of Quantum Complexity
A recently proposed quantum mechanical criterion `concavity of energy' for the second law of thermodynamics is studied also for classical particle systems confined in a bounded region by a potential with a time-dependent coupling constant.…
We consider free fermion systems in arbitrary dimensions and represent the occupation pattern of each eigenstate as a classical binary string. We find that the Kolmogorov complexity of the string correctly captures the scaling behavior of…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
We consider quantum decoherence and entropy increase in early universe cosmology. We first study decoherence in a discrete bipartite quantum system for which a single qubit gets entangled with an environment and the entropy increase is…
We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter $\gamma$. This construction deeply relies on the link between black holes and…
We study the classical second law of black hole thermodynamics, for Lovelock theories (other than General Relativity), in arbitrary dimensions. Using the standard formula for black hole entropy, we construct scenarios involving the merger…
A classical and quantum mechanical generalized second law of thermodynamics in cosmology implies constraints on the effective equation of state of the universe in the form of energy conditions, obeyed by many known cosmological solutions,…
Classical thermodynamics is unrivalled in its range of applications and relevance to everyday life. It enables a description of complex systems, made up of microscopic particles, in terms of a small number of macroscopic quantities, such as…
The second law of thermodynamics states that for a thermally isolated system entropy never decreases. Most physical processes we observe in nature involve variations of macroscopic quantities over spatial and temporal scales much larger…
I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon "degrees of freedom"; is finite because the deep structure of spacetime is discrete; is "objective" thanks to the distinguished coarse…
We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume…
We review our approach to the second law of thermodynamics, viewed as a theorem asserting the growth of the mean (Gibbs-von Neumann) entropy of quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic…
Black holes exist all over our Universe, possessing a very wide range of masses. At the moment, they serve as a probe to test general relativity at astrophysical scales, but in the future they may also give us information about gravity at…
We propose a new form of the Second Law inequality that defines a tight bound for extractable work from the non-equilibrium quantum state. In classical thermodynamics, the optimal work is given by the difference of free energy, what…
We develop a theory of classical complexity. We study the relations between classical complexity and entropy, and conjecture that in an isolated system, classical absolute complexity always tends to grow, until it reaches its maximum. We…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
Black hole thermodynamics provides a unique setting in which general relativity, quantum field theory, and statistical mechanics converge. In semiclassical gravity, this interplay culminates in the generalized second law (GSL), whose modern…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…