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Order versus disorder in the structure of materials plays a key role in the theoretical prediction of their properties. However, this structural description appears to be ineffective for new families of materials such as high entropy alloys…

Living systems maintain or increase local order by working against the Second Law of Thermodynamics. Thermodynamic consistency is restored as they dissipate heat, thereby increasing the net entropy of their environment. Recently introduced…

The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…

Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity…

Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

Phases that go beyond dipolar ordering and into multipolar ordering have recently been observed in magneto-electric materials. The resulting phase diagram is commonly explained using the concept of competing orders and exact microscopic…

Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…

Solutes added to solutions often dramatically impact molecular processes ranging from the suspension or precipitation of colloids to biomolecular associations and protein folding. Here we revisit the origins of the effective attractive…

The field of high entropy oxides (HEOs) flips traditional materials science paradigms on their head by seeking to understand what properties arise in the presence of profound configurational disorder. This disorder, which originates from…

Closely related to the laws of thermodynamics, the detection and quantification of disequilibria are crucial in unraveling the complexities of nature, particularly those beneath observable layers. Theoretical developments in nonequilibrium…

The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…

In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…

The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive…

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…

Non-equilibrium and equilibrium thermodynamics of an interacting component in a relativistic multi-component system is discussed covariantly by exploiting an entropy identity. The special case of the corresponding free component is…

In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…

Random non-reciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system towards pattern formation. The enhanced stability is an exact result when the number of species approaches…