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A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…

Dynamical Systems · Mathematics 2013-05-28 Sarah Tumasz , Jean-Luc Thiffeault

We investigate how the dynamical production of quantum entanglement for weakly coupled, composite quantum systems is influenced by the chaotic dynamics of the corresponding classical system, using coupled kicked tops. The linear entropy for…

Quantum Physics · Physics 2009-11-07 Hiroshi Fujisaki , Takayuki Miyadera , Atushi Tanaka

We introduce the concept of \(k\)-type entropy for dynamical systems generated by \(\mathbb{Z}^d\)-actions on compact metric spaces. We investigate its fundamental properties and establish connections with classical entropy and other…

Dynamical Systems · Mathematics 2025-11-24 Anshid Aboobacker , Sharan Gopal

According to a previous conjecture, spatial and temporal Lyapunov exponents of chaotic extended systems can be obtained from derivatives of a suitable function: the entropy potential. The validity and the consequences of this hypothesis are…

chao-dyn · Physics 2009-10-30 Stefano Lepri , Antonio Politi , Alessandro Torcini

We consider several low--dimensional chaotic maps started in far-from-equilibrium initial conditions and we study the process of relaxation to equilibrium. In the case of conservative maps the Boltzmann-Gibbs entropy S(t) increases linearly…

Statistical Mechanics · Physics 2007-05-23 M. Baranger , V. Latora , A. Rapisarda

Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom…

For dynamical systems satisfying the approximate $\mathbb{Z}^{d}$ or $\mathbb{Z}_+^{d}$-product property and asymptotically entropy expansiveness, we establish a precise description of the structure of their space of invariant measures. In…

Dynamical Systems · Mathematics 2026-05-21 Yage Liu , Ercai Chen , Xiaoyao Zhou

In this paper, we introduce the notions of topological pressure and measure-theoretic entropy for a free semigroup action. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a…

Dynamical Systems · Mathematics 2016-10-27 Xiaogang Lin , Dongkui Ma , Yupan Wang

For an expansive homeomorphism, we investigate the relationship among dimension, entropy, and Lyapunov exponents. Motivated by Young's formula for surface diffeomorphisms, which links dimension and measure-theoretic entropy with hyperbolic…

Dynamical Systems · Mathematics 2025-09-09 Ercai Chen , Tassilo Küpper , Yunxiang Xie

Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…

Mathematical Physics · Physics 2025-08-26 Hong Qian , Zhongwei Shen

In order to understand the Landau-Lifshitz conjecture on the relationship between quantum measurements and the thermodynamic second law, we discuss the notion of ``diabatic'' and ``adiabatic'' forces exerted by the quantum object on the…

Quantum Physics · Physics 2009-10-31 Y. N. Srivastava , G. Vitiello , A. Widom

The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…

Soft Condensed Matter · Physics 2009-10-31 Paolo Allegrini , Jack F. Douglas , Sharon C. Glotzer

We consider topological dynamical systems given by skew products $S\rtimes_{\tau} T$, where $S\colon Y\to Y$ is a subshift, $\tau\colon Y\to\mathbb{Z}$ is a continuous cocycle, and $T$ is an arbitrary invertible topological system. For…

Dynamical Systems · Mathematics 2025-06-24 Nicanor Carrasco-Vargas

Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a…

Statistical Mechanics · Physics 2017-10-17 Jannik Ehrich , Andreas Engel

As quantum analogs of the classical Kolmogorov-Sinai entropy, quantum dynamical entropies have emerged as important tools to characterize complex quantum dynamics. In particular, Alicki-Fannes-Lindblad (AFL) entropy, which quantifies the…

Quantum Physics · Physics 2025-10-22 Eric D. Schultz , Keiichiro Furuya , Laimei Nie

Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…

Statistical Mechanics · Physics 2026-03-31 Tuan Pham , Deepak Gupta

Using free probability constructions involving Cuntz-Pimsner C*-algebras we show that the topological entropy of the free product of two automorphisms is equal to the maximum of the individual entropies. As applications we show that general…

Operator Algebras · Mathematics 2007-05-23 N. P. Brown , K. Dykema , D. Shlyakhtenko

For classical nonequilibrium systems, the separation of the total entropy production into the adiabatic and nonadiabatic contributions is useful for understanding irreversibility in nonequilibrium thermodynamics. In this article, we…

Statistical Mechanics · Physics 2015-06-16 Jordan M. Horowitz , Juan M. R. Parrondo

We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid…

Statistical Mechanics · Physics 2017-05-15 Juan M. R. Parrondo , Christian van den Broeck , Ryoichi Kawai

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of…

Quantum Physics · Physics 2021-08-26 Akira Sone , Sebastian Deffner