Related papers: More Really is Different
The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems. In our work, we investigate the relationship between higher-order…
Relating macroscopic observables to microscopic interactions is a central challenge in the study of complex systems. While current approaches often focus on pairwise interactions, a complete understanding requires going beyond these to…
An elementary understanding of the relevant length, mass and energy scales at the molecular level can be used to explain the order of magnitude of material properties such as mass density, latent heat, surface tension, elastic moduli and…
Real-world systems are characterized by complex interactions of their internal degrees of freedom, while living in ever-changing environments whose net effect is to act as additional couplings. Here, we introduce a paradigmatic interacting…
A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence $x$ over a finite alphabet is ultimately periodic if and only if, for some $n$, the number of different factors of length $n$ appearing in $x$ is less than…
Life occurs in concentrated `Ringer Solutions' derived from seawater that Lesser Blum studied for most of his life. As we worked together, Lesser and I realized that the questions asked of those solutions were quite different in biology…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
Disordered many-body systems exhibit a wide range of emergent phenomena across different scales. These complex behaviors can be utilized for various information processing tasks such as error correction, learning, and optimization. Despite…
In material science, it was established that as the number of particles $ N $ in a material gets more and more, especially in the thermodynamic limit, various macroscopic quantum phenomena such as superconductivity, superfluidity, quantum…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
In his seminal work in the 1970s, Robert May suggested that there is an upper limit to the number of species that can be sustained in stable equilibrium by an ecosystem. This deduction was at odds with both intuition and the observed…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Entanglement is known to be a relative notion, defined with respect to the choice of physical observables to be measured (i.e., the measurement setup used). This implies that, in general, the same state can be both separable and entangled…
In attempting to derive irreversible macroscopic thermodynamics from reversible microscopic dynamics, Boltzmann inadvertently smuggled in a premise that assumed the very irreversibility he was trying to prove: 'molecular chaos.' The program…
Physical laws are a set of rules in the relationship between observations made by the experimenter. All these observations are made through a mechanism that links the external world to the experimenter's awareness, a mechanism which is not…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
Arising out of an attempt at a new foundations of mathematics, in which relations are more primitive than sets, and out of the theoretical physicists' concept of underlying causes of empirical phenomena, the idea of a purely mathematical…
Traversals of data structures are ubiquitous in programming. Consequently, it is important to be able to characterise those structures that are traversable and understand their algebraic properties. Traversable functors have been…
Irreversibility remains one of the least understood concepts in physics. One of the main reasons is the fact that the fundamental laws of classical and quantum physics are time symmetric, whereas macroscopic processes evolve in a preferred…
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…