Dear Colleagues,

Processes with memory are pervasive in many areas of natural and social sciences. Examples include classical physics and quantum physics, thermodynamics and statistical physics, continuum mechanics, economics and finance, computer science and information theory, biology and psychology, chaotic and self-organization processes, modern mathematics. The term memory identifies a property that characterizes the dependence of the process state at a given time on the history of state changes in the past.

The first description of physical processes with memory was given by Ludwig Boltzmann, when he proposed a physical model of isotropic viscoelastic media. He also proposed the linear superposition principle and the memory fading principle for processes with memory. The fading of memory means that it is less probable to expect a strengthening of the memory with respect to the most distant events. The Boltzmann theory has been significantly developed by Vito Volterra in the form of the heredity concept and its application to natural sciences. Volterra made a significant contribution to the development of the theory of integral equations, which is an important mathematical instrument to describe processes with memory. In different areas, scientists have empirically observed long-range time dependencies, for which the correlations between observations decay to zero more slowly than it can be expected from independent data or data resulting from classical Markov and ARMA models. Processes with long memory are characterized by slowly decaying autocorrelations or a spectral density that has a pole at the origin.

In modern sciences, integro-differential equations are actively used to describe processes with memory. A wide class of integral and integro-differential equations refers to fractional calculus that studies equations with derivatives and integrals of non-integer orders. Applications of fractional calculus and equations with derivatives and differences of non-integer orders are currently widely used tools for describing processes with memory.

This Special Issue focuses on original and new research results on the theory of processes with memory in natural and social sciences, when the state of the process at a given time depends on the history of state changes in the past. We welcome manuscripts devoted both to new problems and to new results, as well as reviews of existing methods, models, and processes. Manuscripts are required offering models describing processes with memory and developing a mathematical apparatus that allows describing such processes in various fields of science. We welcome manuscripts devoted to the description of the role of the concept of entropy and related methods in processes with fading memory, i.e., in forgetting past states of processes.

Papers may be devoted to the following (and related) topics:

• Non-equilibrium statistical physics
• Open quantum systems
• Quantum computing
• Continuum mechanics and electrodynamics  
• Material sciences
• Econophysics
• Financial processes
• Economy dynamics
• Computer sciences
• Biological processes and bioinformatics
• Mathematical psychology
• Applied linguistics
• Complex processes
• Nonlinear dynamics
• Fractional calculus and its applications
• Non-Markovian processes
• Integral and integro-differential equations
• Deterministic chaos
• Self-organization processes
• Time series
• Signal processing

Prof. Dr. Vasily E. Tarasov
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• memory
• dissipation
• entropy
• open quantum systems
• chaos
• self-organization
• adaptation
• econophysics
• economics
• finance
• power laws
• nonequilibrium states
• time series