Related papers: Undecidability, entropy and information loss in co…
We compare the thermodynamic entropy of a quantum Brownian oscillator derived from the partition function of the subsystem with the von Neumann entropy of its reduced density matrix. At low temperatures we find deviations between these two…
We consider the statistical irreversibility and its compatibility with the reversible dynamics. The role played by the observation is analyzed in detail. It makes our previous proof for the second law of thermodynamics clearer. On this…
The uncertainty principle is an important principle in quantum theory. Based on this principle, it is impossible to predict the measurement outcomes of two incompatible observables, simultaneously. Uncertainty principle basically is…
The thermodynamic uncertainty relation quantifies a trade-off between the relative fluctuations of trajectory currents and the thermodynamic cost, indicating that the current precision is fundamentally constrained by entropy production. In…
In the above mentioned paper by J. Dunkel and S. A. Trigger [Phys. Rev. {\bf A 71}, 052102, (2005)] a hypothesis has been pursued that the loss of information associated with the quantum evolution of pure states, quantified in terms of an…
We explore the dynamics of information systems. We show that the driving force for information dynamics is determined by both the information landscape and information flux which determines the equilibrium time reversible and the…
We provide a unified thermodynamic formalism describing information transfers in autonomous as well as nonautonomous systems described by stochastic thermodynamics. We demonstrate how information is continuously generated in an auxiliary…
The second law of classical thermodynamics, based on the positivity of the entropy production, only holds for deterministic processes. Therefore the Second Law in stochastic quantum thermodynamics may not hold. By making a fundamental…
Information decompositions quantify how the Shannon information about a given random variable is distributed among several other random variables. Various requirements have been proposed that such a decomposition should satisfy, leading to…
The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon…
Quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical…
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$…
A possible solution of the information paradox can be sought in quantum information scrambling. In this paradigm, it is postulated that all information entering a black hole is rapidly and chaotically distributed across the event horizon…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
New concepts from nonequilibrium thermodynamics are used to show that Landauer's principle can be understood in terms of time asymmetry in the dynamical randomness generated by the physical process of the erasure of digital information. In…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…