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This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…
The quantum model of the brain proposed by Ricciardi and Umezawa is extended to dissipative dynamics in order to study the problem of memory capacity. It is shown that infinitely many vacua are accessible to memory printing in a way that in…
We derive an expression for the equilibrium probability distribution of a quantum state in contact with a noisy thermal environment that formally separates contributions from quantum and classical forms of probabilistic uncertainty. A…
We study the thermodynamic cost associated with the erasure of one bit of information over a finite amount of time. We present a general framework for minimizing the average work required when full control of a system's microstates is…
This paper introduces time into information theory, gives a more accurate definition of information, and unifies the information in cognition and Shannon information theory. Specially, we consider time as a measure of information, giving a…
Random Boolean networks are models of disordered causal systems that can occur in cells and the biosphere. These are open thermodynamic systems exhibiting a flow of energy that is dissipated at a finite rate. Life does work to acquire more…
Synapses are information efficient in the sense that their natural conductance values convey as many bits per Joule as possible, but efficiency falls rapidly if the conductance is forced to deviate from its natural value (Harris et al,…
In recent years, machine learning neural network has penetrated deeply into people's life. As the price of convenience, people's private information also has the risk of disclosure. The "right to be forgotten" was introduced in a timely…
Landauer discussed the minimum energy necessary for computation and stated that erasure of information is accompanied by heat generation to the amount of kT ln2/bit. Modifying the above statement, we claim that erasure of information is…
Forgetfulness is a common feature of nature. Moreover, without forgetfulness, repeatability would be impossible. Despite this, small systems constantly leak information about their state to their surroundings, and quantum mechanics tells us…
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…
A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezing $\d S<0$ of its entropy must release at least an amount $|\dbarrm Q|=T|\d S|$ of heat. This serves as a basis for the Landauer principle, which…
We explore the problem of selectively forgetting a particular subset of the data used for training a deep neural network. While the effects of the data to be forgotten can be hidden from the output of the network, insights may still be…
Second law of thermodynamics can be apparently violated for systems whose dynamics depends on acquired information by measurement. However, when one consider measurement and erasure process together along with the system it saves the second…
Classical and quantum error correction are presented in the form of Maxwell's demon and their efficiency analyzed from the thermodynamic point of view. We explain how Landauer's principle of information erasure applies to both cases. By…
Motivated by the recent proposed models of the information engine [D. Mandal and C. Jarzynski, Proc. Natl. Acad. Sci. 109, 11641 (2012)] and the information refrigerator [D. Mandal, H. T. Quan, and C. Jarzynski, Phys. Rev. Lett. 111, 030602…
The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored…
Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy. We set up here a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems,…
In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework…
This article considers the performance of digital communication systems transmitting messages over finite-state erasure channels with memory. Information bits are protected from channel erasures using error-correcting codes; successful…