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For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion…
Suppose that you have $n$ colours and $m$ mutually independent dice, each of which has $r$ sides. Each dice lands on any of its sides with equal probability. You may colour the sides of each die in any way you wish, but there is one…
This chapter concerns "control volume analysis", the standard engineering tool for the analysis of flow systems, and its application to entropy balance calculations. Firstly, the principles of control volume analysis are enunciated and…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics…
Shannon entropy for discrete distributions is a fundamental and widely used concept, but its continuous analogue, known as differential entropy, lacks essential properties such as positivity and compatibility with the discrete case. In this…
In an essential and quite general setup, based on networks, we identify Schnakenberg's observables as the constraints that prevent a system from relaxing to equilibrium, showing that, in the linear regime, steady states satisfy a minimum…
High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…
The entropy region is constructed from vectors of random variables by collecting Shannon entropies of all subvectors. Its shape is studied here by means of polymatroidal constructions, notably by convolution. The closure of the region is…
We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has…
A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a…
A maximum entropy dissipation problem at a traffic junction and the corresponding coupling condition are studied. We prove that this problem is equivalent to a coupling condition introduced by Holden and Risebro. An $L^1$-contraction…
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to…
We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
Max stable laws are limit laws of linearly normalized partial maxima of indepen- dent, identically distributed (iid) random variables (rvs). These are analogous to stable laws which are limit laws of normalized partial sums of iid rvs. In…
This paper is concerned with a set of novel coupling conditions for the $3\times 3$ one-dimensional Euler system with source terms at a junction of pipes with possibly different cross-sectional areas. Beside conservation of mass, we require…
As two of the most important entanglement measures--the entanglement of formation and the entanglement of distillation--have so far been limited to bipartite settings, the study of other entanglement measures for multipartite systems…