Related papers: Thermodynamic-Complexity Duality: Embedding Comput…
A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et…
The third law of thermodynamics forbids cooling a physical system to absolute zero in a finite number of operational steps. Although this unattainability principle has been quantified for specific state-to-state transitions, a universal,…
Irreversible information processing cannot be carried out without some inevitable thermodynamical work cost. This fundamental restriction, known as Landauer's principle, is increasingly relevant today, as the energy dissipation of computing…
Computation, if treated as a set of physical processes that act on information represented by states of matter, encompasses biological systems, digital systems, and other constructs, and may be a fundamental measure of living systems. The…
An open question of fundamental importance in quantum thermodynamics is how to describe the statistics of work for initial state with quantum coherence. In this paper, work statistics is considered from a fully new perspective of…
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
Defining similarity is a fundamental challenge in information science. Watanabe's Ugly Duckling Theorem highlights diversity, while algorithmic information theory emphasizes depth through Information Distance. We propose a…
The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix,…
Information-processing systems that coordinate multiple agents and objectives face fundamental thermodynamic constraints. We show that solutions with maximum utility to act as coordination focal points have a much higher selection pressure…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
Cosmological perturbation equations derived from low-energy effective actions are shown to be invariant under a duality transformation reminiscent of electric-magnetic, strong-weak coupling, S-duality. A manifestly duality-invariant…
Algorithmic entropy can be seen as a special case of entropy as studied in statistical mechanics. This viewpoint allows us to apply many techniques developed for use in thermodynamics to the subject of algorithmic information theory. In…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
We initiate a rigorous study of computational entanglement theory, inspired by the emerging usefulness of ideas from quantum information theory in computational complexity. We define new operational computational measures of entanglement --…
Information processing typically occurs via the composition of modular units, such as universal logic gates. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex global…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number…
Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…