Related papers: Partition function approach to non-Gaussian likeli…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as…
We review of the interface between (theoretical) physics and information for non-experts. The origin of information as related to the notion of entropy is described, first in the context of thermodynamics then in the context of statistical…
We expand upon a natural analogy between Bayesian statistics and statistical physics in which sample size corresponds to inverse temperature. This analogy motivates the definition of two novel statistical quantities: a learning capacity and…
We study the informational underpinnings of thermodynamics and statistical mechanics, using an abstract framework, general probabilistic theories, capable of describing arbitrary physical theories. This allows one to abstract the…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
Thermodynamic properties can be in principle derived from the partition function, which, in many-atom systems, is hard to evaluate as it involves a sum on the accessible microscopic states. Recently, the partition function has been computed…
At this point in time, two major areas of physics, statistical mechanics and quantum mechanics, rest on the foundations of probability and entropy. The last century saw several significant fundamental advances in our understanding of the…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
This paper provides a perspective on applying the concepts of information thermodynamics, developed recently in non-equilibrium statistical physics, to problems in theoretical neuroscience. Historically, information and energy in…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
The fundamentals of Statistical Mechanics require a fresh definition in the context of the developments in Classical Mechanics of integrable and chaotic systems. This is done with the introduction of Micro Partitions ; a union of disjoint…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…
The problem of the insensitivity of the macroscopic behavior of any thermodynamical system to partitioning generates a bias between the reproducibility of its macroscopic behavior viewed as the simplest form of causality and its long-term…
We show that model-based Bayesian clustering, the probabilistically most systematic approach to the partitioning of data, can be mapped into a statistical physics problem for a gas of particles, and as a result becomes amenable to a…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…