We develop notions of Rota–Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin’s renormalization and computation program, to Markov random fields and to counting functions and zeta...

This talk provides a natural continuation of the talk presented by Andreas Fring in this conference. Part I was focused on explaining how the DC conductance for a free Fermion theory in the presence of different kinds of defects can be computed by evaluating the Kubo formula. In this talk I will focus on an alternative method for the computation of the same quantity, that is the evaluation of L...

⋆ It seems very unlikely that quantum computation can be realized unless there is some means of correcting the errors which will inevitably arise when physical devices are constructed to carry out such a computation. The situation is far different from that in ordinary “classical” computers in which for most purposes the probabilities of errors are so small that they can be ignored. • The absen...

We discuss the fundamental limits of computing using a new paradigm for quantum computation, cellular automata composed of arrays of Coulombically coupled quantum dot molecules, which we term quantum cellular automata (QCA). Any logical or arithmetic operation can be performed in this scheme. QCA’s provide a valuable concrete example of quantum computation in which a number of fundamental issue...

In “Is the Frobenius Matrix Norm Induced?”, the authors ask whether the Frobenius and the norms are induced. There, they claimed that the Frobenius norm is not induced and, consequently, conjectured that the norm may not be induced. In this note, it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the norm is in fact induced on a particular matrix-v...

We present an algorithm to evaluate large deviation functions associated to historydependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm valuable for systems with multiple time scales, thus extending the work of Giardinà, Kurchan and Peliti [1]. The procedure is supplemented with a thermodynamic-in...

This paper proposes that intelligent processes can be completely explained by thermodynamic principles. They can equally be described by information-theoretic principles that, from the standpoint of the required optimizations, are functionally equivalent. The underlying theory arises from two axioms regarding distinguishability and causality. Their consequence is a theory of computation that ap...