Related papers: Entropy and perpetual computers
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
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…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…
This paper is the second part of a previous paper (Marquet, 2019) dealing with the need to define the entropy with an absolute way, by using the third law of thermodynamics. In this second part it is shown that there is a need and interest…
The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates…
We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks. Subsequently, one can use virtually any machine learning classification algorithm for…
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…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
I give a quick overview of some of the theoretical background necessary for using modern non-equilibrium statistical physics to investigate the thermodynamics of computation. I first present some of the necessary concepts from information…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
Comparison-based algorithms are algorithms for which the execution of each operation is solely based on the outcome of a series of comparisons between elements. Comparison-based computations can be naturally represented via the following…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…