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Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…
Dynamic spin correlation functions $<S_i^x (t)S_j^x>$ for the 1D $S=1/2$ $XX$ model $H = -J\Sigma_i \{S_i^x S_{i+1}^x + S_i^y S_{i+1}^y \}$ are calculated exactly for finite open chains with up to N=10000 spins. Over a certain time range…
We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal…
The study of inter-human communication requires a more complex framework than Shannon's (1948) mathematical theory of communication because "information" is defined in the latter case as meaningless uncertainty. Assuming that meaning cannot…
We numerically investigate classical and quantum correlations in one-dimensional quantum critical systems. The infinite matrix product state (iMPS) representation is employed in order to consider an infinite-size spin chain. By using the…
Warning: this paper contains content that may be offensive or upsetting. Language has the power to reinforce stereotypes and project social biases onto others. At the core of the challenge is that it is rarely what is stated explicitly, but…
Human language has a distinct systematic structure, where utterances break into individually meaningful words which are combined to form phrases. We show that natural-language-like systematicity arises in codes that are constrained by a…
According to conventional wisdom electric double-layer forces normally decay exponentially with separation distance. Here we present experimental evidence of algebraically decaying double-layer interactions. We show that algebraic…
Natural language is a complex system that exhibits robust statistical regularities. Here, we represent text as a trajectory in a high-dimensional embedding space generated by transformer-based language models, and quantify scale-dependent…
The making of knowledge engines in natural language processing has been shaped by two seemingly distinct paradigms: one grounded in structure, the other driven by massively available unstructured data. The structured paradigm leverages…
Correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system, widely used in many-body physics and in quantum information science, respectively. We find that…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…
It is generally believed that, when a linguistic item acquires a new meaning, its overall frequency of use in the language rises with time with an S-shaped growth curve. Yet, this claim has only been supported by a limited number of case…
Mutual information is a widely-used information theoretic measure to quantify the amount of association between variables. It is used extensively in many applications such as image registration, diagnosis of failures in electrical machines,…
For the study of information propagation, one fundamental problem is uncovering universal laws governing the dynamics of information propagation. This problem, from the microscopic perspective, is formulated as estimating the propagation…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of that sentence. To do so, we exploited the perfect structural match of grammar and…
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the…