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This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address inferential questions arising in a wide range of…
We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of…
In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat…
Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…
An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks,…
We generalize the method introduced in J. Phys. A: Math. Gen. 35, 7255 (2002) based on the concept of thermodynamic equivalence and we transform a Fermi system of general density of states into a thermodynamically equivalent Bose system.…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics…
In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines,…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
The behavior of a collection of identical particles is intimately linked to the symmetries of their wavefunction under particle exchange. Topological anyons, arising as quasiparticles in low-dimensional systems, interpolate between bosons…