in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

The pillars of quantum theory include entanglement and operators' failure to commute. Page curve quantifies the bipartite a many-body system in random pure state. This is known decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail other, are current interest thermodynamics. For example, noncommuting charges were show...

We introduce a generalized approach to characterize the non-Markovianity of quantum dynamical maps via breakdown monotonicity thermodynamic functions. By adopting an entropy-based formulation thermodynamics, we use relationship between heat and entropy propose measure based on flow for single-qubit evolutions. This can be applied unital that do not invert sign internal energy. Under certain con...

Entropy is a great tool in thermodynamics and statistical physics [...]

We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry using correlation matrix technique. Our results show that entropy has a logarithmic correction to area law in both one-dimensional and two-dimensional systems. For any one-band system, we prove each Fermi point system contributes exactly 1/2 coefficient c correction. Moreover, this relation bet...