Algorithmic information and simplicity in statistical physics
نویسنده
چکیده
Given a list of N states with probabilities 0 < p1 ≤ · · · ≤ pN , the average conditional algorithmic information Ī to specify one of these states obeys the inequality H ≤ Ī < H + O(1), where H = − pj log2 pj and O(1) is a computer-dependent constant. We show how any universal computer can be slightly modified in such a way that the inequality becomes H ≤ Ī < H + 1, thereby eliminating the computer-dependent constant from statistical physics.
منابع مشابه
Probabilistic Sufficiency and Algorithmic Sufficiency from the point of view of Information Theory
Given the importance of Markov chains in information theory, the definition of conditional probability for these random processes can also be defined in terms of mutual information. In this paper, the relationship between the concept of sufficiency and Markov chains from the perspective of information theory and the relationship between probabilistic sufficiency and algorithmic sufficien...
متن کاملReality as simplicity
We discuss some fundamental aspects of information theory and its relationship to physics and neuroscience. The aim is to identify some questions and point out the relevance of the concept of Kolmogovov complexity in their eventual resolution. The discussion is based on two premises: 1) all human experience is generated in the brain, 2) all the brain has access to is information. Taken together...
متن کاملWe Must Choose the Simplest Physical Theory Levin Li Vit Anyi Theorem and Its Potential Physical Applications
If several physical theories are consistent with the same experimental data which theory should we choose Physicists often choose the simplest theory this principle explicitly formulated by Occam is one of the basic principles of physical reasoning However until recently this principle was mainly a heuristic because it uses the informal notion of simplicity With the explicit notion of simplicit...
متن کاملAnalysis of Information and Computation in Physics Explains Cognitive Paradigms: from Full Cognition to Laplace Determinism to Statistical Determinism to Modern Approach
In this paper, we analyze the problem of prediction in physics from the computational viewpoint. We show that physical paradigms like Laplace determinism, statistical determinism, etc., can be naturally explained by this computational analysis. In our explanations, we use the notions of the Algorithmic Information Theory such as Kolmogorov complexity and algorithmic randomness, as well as the n...
متن کاملThe Role of Algorithmic Applications in the Development of Architectural Forms (Case Study:Nine High-Rise Buildings)
The process of developing architectural forms has greatly been changed by advances in digital technology, especially in design tools and applications. In recent years, the advent of graphical scripting languages in the design process has profoundly affected 3D modeling. Scripting languages help develop algorithms and geometrical grammar of shapes based on their constituent parameters. This stud...
متن کامل