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We determine asymptotically the two extremal constructions for the tiling problem of the $H$-shaped tree. In particular, the first extremal construction is close to the complement of two cliques, in contrast to previously studied bipartite…
It is up to now a challenge to control the conduction of heat. Here we develop a method to distort the temperature distribution signature of an object at will. As a result, the object accurately exhibits the same temperature distribution…
A review is given on the thermodynamical structure of bipartite entanglement. By comparing it to the axiomatic formulation of thermodynamics presented by Giles it is shown that for finite dimensional systems the two theories are formally…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve…
We compare two henselisations of a residually discrete valuation domain. Our constructive proof that a certain natural morphism is an isomorphism is also a proof in classical mathematics. Although this isomorphism is implicitly accepted as…
Whenever graphs admit equitable partitions, their quotient graphs highlight the structure evidenced by the partition. It is therefore very natural to ask what can be said about two graphs that have the same quotient according to certain…
Matrix acidization is an important technique to enhance oil production at the tertiary recovery stage, and its numerical simulation is never concluded. From one of the earliest models, i.e. the two-scale model (Darcy framework), the…
Starting from the observation that distinct notions of copying have arisen in different categorical fields (logic and computation, contrasted with quantum mechanics) this paper addresses the question of when, or whether, they may coincide.…
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue…
We show the robustness of the structure of Legendre transform in thermodynamics against the replacement of the standard linear average with the Kolmogorov-Nagumo nonlinear average to evaluate the expectation values of the macroscopic…
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
In this paper, we prove that the self-dual morphological hierarchical structure computed on a n-D gray-level wellcomposed image u by the algorithm of G{\'e}raud et al. [1] is exactly the mathematical structure defined to be the tree of…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
We return to the question of how the choice of stabilizer generators affects the preservation of information on structures whose degenerate ground state encodes a classical redundancy code. Controlled-not gates are used to transform the…
We introduce a method "DMT" for approximating density operators of 1D systems that, when combined with a standard framework for time evolution (TEBD), makes possible simulation of the dynamics of strongly thermalizing systems to arbitrary…
Statistical mechanics assumes that a quantum many-body system at low temperature can be effectively described by its Gibbs state. However, many complex quantum systems exist only as metastable states of dissipative open system dynamics,…
This is the fourth article about the isomorphism between Lubin-Tate and Drinfeld towers. We prove the final result concerning the isomorphism that is to say the existence of an equivariant isomorphism between some blow-up of the formal…
Thermal rectification which is a diode-like behavior of heat flux has been studied over a long time. However, a universal and systematic physical description is still lacking. In this letter, a perturbation theory of thermal rectification…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…