Systolic aspects of black hole entropy

We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3+1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections $\Sigma$ of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of $\Sigma$ are violated in quantum theory. We choose the systoles of $\Sigma$ to encode its complexity, which gives rise to the black hole entropy. We present hand-waving reasons why the entropy of the black hole can be considered as a function of the volume entropy of $\Sigma$. We focus on the limiting case of $\Sigma$ having a large genus.Comment: 20 pages. No figures. LaTeX2e. This version: change of the author's affiliation. Other minor changes. To be published in a Special Issue of "Axioms" on "Theory and Mathematical Aspects of Black Holes

Estimating topological entropy from the motion of stirring rods

Stirring a two-dimensional viscous fluid with rods is often an effective way to mix. The topological features of periodic rod motions give a lower bound on the topological entropy of the induced flow map, since material lines must `catch' on the rods. But how good is this lower bound? We present examples from numerical simulations and speculate on what affects the 'gap' between the lower bound and the measured topological entropy. The key is the sign of the rod motion's action on first homology of the orientation double cover of the punctured disk.Comment: 10 pages, 20 figures. IUTAM Procedia style (included). Submitted to volume "Topological Fluid Dynamics II.

Normalized entropy density of the 3D 3-state Potts model

Using a multicanonical Metropolis algorithm we have performed Monte Carlo simulations of the 3D 3-state Potts model on $L^3$ lattices with L=20, 30, 40, 50. Covering a range of inverse temperatures from $\beta_{\min}=0$ to $\beta_{\max}=0.33$ we calculated the infinite volume limit of the entropy density $s(\beta)$ with its normalization obtained from $s(0)=\ln 3$. At the transition temperature the entropy and energy endpoints in the ordered and disordered phase are estimated employing a novel reweighting procedure. We also evaluate the transition temperature and the order-disorder interface tension. The latter estimate increases when capillary waves are taken into account.Comment: 5 pages, 4 figure

How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem

We analyze cosmology assuming unitary quantum mechanics, using a tripartite partition into system, observer and environment degrees of freedom. This generalizes the second law of thermodynamics to "The system's entropy can't decrease unless it interacts with the observer, and it can't increase unless it interacts with the environment." The former follows from the quantum Bayes Theorem we derive. We show that because of the long-range entanglement created by cosmological inflation, the cosmic entropy decreases exponentially rather than linearly with the number of bits of information observed, so that a given observer can reduce entropy by much more than the amount of information her brain can store. Indeed, we argue that as long as inflation has occurred in a non-negligible fraction of the volume, almost all sentient observers will find themselves in a post-inflationary low-entropy Hubble volume, and we humans have no reason to be surprised that we do so as well, which solves the so-called inflationary entropy problem. An arguably worse problem for unitary cosmology involves gamma-ray-burst constraints on the "Big Snap", a fourth cosmic doomsday scenario alongside the "Big Crunch", "Big Chill" and "Big Rip", where an increasingly granular nature of expanding space modifies our life-supporting laws of physics. Our tripartite framework also clarifies when it is valid to make the popular quantum gravity approximation that the Einstein tensor equals the quantum expectation value of the stress-energy tensor, and how problems with recent attempts to explain dark energy as gravitational backreaction from super-horizon scale fluctuations can be understood as a failure of this approximation.Comment: Updated to match accepted PRD version, including Quantum Bayes Theorem derivation and rigorous proof that decoherence increases von Neumann entropy. 20 pages, 5 fig

Entropy generation analysisfor the design optimizationof solid oxide fuel cells

Purpose - The aim of this paper is to investigate performance improvements of a monolithic solid oxide fuel cell geometry through an entropy generation analysis. Design/methodology/approach - The analysis of entropy generation rates makes it possible to identify the phenomena that cause the main irreversibilities in the fuel cell, to understand their causes and to propose changes in the design and operation of the system. The various contributions to entropy generation are analyzed separately in order to identify which geometrical parameters should be considered as the independent variables in the optimization procedure. The local entropy generation rates are obtained through 3D numerical calculations, which account for the heat, mass, momentum, species and current transport. The system is then optimized in order to minimize the overall entropy generation and increase efficiency. Findings - In the optimized geometry, the power density is increased by about 10 per cent compared to typical designs. In addition, a 20 per cent reduction in the fuel cell volume can be achieved with less than a 1 per cent reduction in the power density with respect to the optimal design. Research limitations/implications - The physical model is based on a simple composition of the reactants, which also implies that no chemical reactions (water gas shift, methane steam reforming, etc.) take place in the fuel cell. Nevertheless, the entire procedure could be applied in the case of different gas compositions. Practical implications - Entropy generation analysis allows one to identify the geometrical parameters that are expected to play important roles in the optimization process and thus to reduce the free independent variables that have to be considered. This information may also be used for design improvement purposes. Originality/value - In this paper, entropy generation analysis is used for a multi-physics problem that involves various irreversible terms, with the double use of this physical quantity: as a guide to select the most relevant design geometrical quantities to be modified and as objective function to be minimized in the optimization proces

Entropy-Area Relations in Field Theory

We consider the contribution to the entropy from fields in the background of a curved time-independent metric. To account for the curvature of space, we postulate a position-dependent UV cutoff. We argue that a UV cutoff on energy naturally implies an IR cutoff on distance. With this procedure, we calculate the scalar contribution in a background anti-de Sitter space, the exterior of a black hole, and de Sitter space. In all cases, we find results that can be simply interpreted in terms of local energy and proper volume, yielding insight into the apparent reduced dimensionality of systems with gravity.Comment: 20 pages, 1 figur