Related papers: Optimizing entropy bounds for macroscopic systems
We explore a recently introduced quantum thermodynamic entropy $S^Q_{univ}$ of a pure state of a composite system-environment computational "universe" with a simple system $\mathcal{S}$ coupled to a constant temperature bath $\mathcal{E}$.…
We call a state ``vacuum bounded'' if every measurement performed outside a specified interior region gives the same result as in the vacuum. We compute the maximum entropy of a vacuum-bounded state with a given energy for a one-dimensional…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
Bekenstein's inequality sets a bound on the entropy of a charged macroscopic body. Such a bound is understood as a universal relation between physical quantities and fundamental constants of nature that should be valid for any physical…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
We construct explicit examples of spontaneous energy generation and non-uniqueness for the compressible Euler system, with and without pressure, by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The…
After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this…
Nonequilibrium processes break time-reversal symmetry and generate entropy. Living systems are driven out-of-equilibrium at the microscopic level of molecular motors that exploit chemical potential gradients to transduce free energy to…
We derive the microcanonical ensemble from the Maximum Entropy Principle (MEP) using the phase space volume entropy of P. Hertz. Maximizing this entropy with respect to the probability distribution with the constraints of normalization and…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
Finite physical systems have only a finite amount of distinct state. This finiteness is fundamental in statistical mechanics, where the maximum number of distinct states compatible with macroscopic constraints defines entropy. Here we show…
It is shown that the classical entropy of the extremal black hole depends on two different limits procedures. If we first take the extremal limit and then the boundary limit, the entropy is zero; if we do it the other way round, we get the…
By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy $S$ of a finite-dimensional system around a non-degenerate critical point of its potential energy $V$. We compare $S$ with…
We consider a self-gravitating system consisting of perfect fluid with spherical symmetry. Using the general expression of entropy density, we extremize the total entropy $S$ under the constraint that the total number of particles is fixed.…
The local entropy of a nonequilibrium system of independent fermions is investigated, and analyzed in the context of the laws of thermodynamics. It is shown that the local temperature and chemical potential can only be expressed in terms of…
We define the topological entropy per unit volume in parabolic PDE's such as the complex Ginzburg-Landau equation, and show that it exists, and is bounded by the upper Hausdorff dimension times the maximal expansion rate. We then give a…
It was shown in a previous work that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. In this paper, we go further and derive…
The entropy of extremal black holes (BHs) is obtained using a continuity argument from extremal quasiblack holes (QBHs). It is shown that there exists a smooth limiting transition in which (i) the system boundary approaches the extremal…
The {\em $s$-energy} is a generating function of wide applicability in network-based dynamics. We derive an (essentially) optimal bound of $(3/\rho s)^{n-1}$ on the $s$-energy of an $n$-agent symmetric averaging system, for any positive…
The existence of the thermodynamic limit in spin systems with short- and long-range interactions is established. We consider the infinite-volume limit with a fixed shape of the system. The variational expressions of the entropy density and…