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We study the dynamics of piecewise affine surface homeomorphisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability…

Dynamical Systems · Mathematics 2009-09-29 Jerome Buzzi

We analyze the equilibrium space of an ideal gas using the formalism of geometrothermodynamics. We introduce the concept of thermodynamic geodesics to show that the equilibrium space around a particular initial state can be divided into two…

General Relativity and Quantum Cosmology · Physics 2024-10-11 Hernando Quevedo

We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…

Dynamical Systems · Mathematics 2024-03-27 Julian Hölz

This paper examines the statistical mechanical and thermodynamical consequences of variable phase-space volume element $h_I=\bigtriangleup x_i\bigtriangleup p_i$. Varying $h_I$ leads to variations in the amount of measured information of a…

General Physics · Physics 2016-11-18 Kevin Vanslette

In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full…

Dynamical Systems · Mathematics 2020-05-25 Dawei Yang , Jinhua Zhang

The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…

Quantum Physics · Physics 2013-11-11 H. S. Karthik , A. R. Usha Devi , J. Prabhu Tej , A. K. Rajagopal

Modern thermodynamic theories can be used to study highly complex quantum dynamics. Here, we experimentally demonstrate that the violation of thermodynamic constraints allows to detect the coupling of a quantum system to a hidden…

Quantum Physics · Physics 2021-03-10 Ivan Henao , Raam Uzdin , Nadav Katz

The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…

Adaptation and Self-Organizing Systems · Physics 2007-10-15 David H. Wolpert

We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the experiment? In a programme to study the nature…

Logic · Mathematics 2009-11-20 E. J. Beggs , J. F. Costa , J. V. Tucker

A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in [Avigad et al. 2010,…

Numerical Analysis · Computer Science 2010-06-03 Stefano Galatolo , Mathieu Hoyrup , Cristóbal Rojas

In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…

General Relativity and Quantum Cosmology · Physics 2016-10-14 Marius Oltean , Luca Bonetti , Alessandro D. A. M. Spallicci , Carlos F. Sopuerta

Basic properties of the unified entropies are examined. The consideration is mainly restricted to the finite-dimensional quantum case. Bounds in terms of ensembles of quantum states are given. Both the continuity in Fannes' sense and…

Quantum Physics · Physics 2011-06-28 Alexey E. Rastegin

Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…

General Physics · Physics 2009-05-04 Yi-Fang Chang

G\'acs' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables…

Statistical Mechanics · Physics 2024-12-03 Aram Ebtekar , Marcus Hutter

In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples.…

Mathematical Physics · Physics 2016-09-29 Hernán Cendra , Sergio Grillo , Maximiliano Palacios Amaya

We present a general framework for thermodynamic limits and its applications to a variety of models. In particular we will identify criteria such that the limits are uniform in a parameter. All results are illustrated with the example of…

Probability · Mathematics 2019-01-28 Christoph Schumacher , Fabian Schwarzenberger , Ivan Veselic

The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is…

Statistical Mechanics · Physics 2020-12-29 Van Tuan Vo , Tan Van Vu , Yoshihiko Hasegawa

Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of…

Quantum Physics · Physics 2021-02-23 Adam Hewgill , Gabriele De Chiara , Alberto Imparato

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

Machine Learning · Computer Science 2023-06-27 Lisa Wimmer , Yusuf Sale , Paul Hofman , Bern Bischl , Eyke Hüllermeier

An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…

Quantum Physics · Physics 2008-02-03 N. J. Cerf , C. Adami