Related papers: The different paths to entropy
Starting from the pioneering works of Shannon and Weiner in 1948, a plethora of works have been reported on entropy in different directions. Entropy-related review work in the direction of statistics, reliability and information science, to…
In a recent paper Andrei N. Soklakov explained the foundations of the Lagrangian formulation of classical particle mechanics by means of Kolmogorov complexity. In the present paper we use some of Soklakov ideas in order to derive the second…
We develop the framework of classical Observational entropy, which is a mathematically rigorous and precise framework for non-equilibrium thermodynamics, explicitly defined in terms of a set of observables. Observational entropy can be seen…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
The second law of nonequilibrium thermodynamics within the open system paradigm (a small system coupled to one or multiple baths) is derived. This is done by showing positivity of entropy production for arbitrary Hamiltonian dynamics for a…
There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics (or even a candidate theory of fundamental physics), but as a theory of how manipulations of a physical system may be used to obtain desired…
In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a…
In this work, Gibbs paradox was discussed from the view of observer. The limitations of real observer are analyzed quantitatively. The entropy of mixing was found to be determined by both the identification ability and the information…
The routine definitions of both entropy, and differential entropy show inconsistencies that make them not reciprocally coherent. We propose a few possible modifications of these quantities so that 1) they no longer show incongruities, 2)…
During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…
How to find unknown distributions is questioned in many pieces of research. There are several ways to figure them out, but the main question is which acts more reasonably than others. In this paper, we focus on the maximum entropy principle…
It is important to be able to calculate the moist-air entropy of the atmosphere with precision. A potential temperature has already been defined from the third law of thermodynamics for this purpose. However, a doubt remains as to whether…
Defining the entropy of classical particles raises a number of paradoxes and ambiguities, some of which have been known for over a century. Several, such as Gibbs' paradox, involve the fact that classical particles are distinguishable, and…
Entropy is critically examined as a fundamental concept in contemporary science and informatics. Although the typical Shannon entropy provides a proper framework for describing the canonical ensemble, it fails to represent adequately the…
A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next,…
This paper discusses the possible relation between entropy and the relaxation time of liquids, in particular glass-forming systems, providing supplementing comments to the paper entitled "A brief critique of the Adam-Gibbs entropy model" by…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…
A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is given both in the finite and…
Entropic cosmology assumes several forms of entropy on the horizon of the universe, where the entropy can be considered to behave as if it were related to the exchange (the transfer) of energy. To discuss this exchangeability, the…