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In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
Biological intelligence emerges from substrates that are slow, noisy, and energetically constrained, yet it performs rapid and coherent inference in open-ended environments. Classical computational theories, built around vector-space…
A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through…
The internal energy of individual subsystems is not well defined in interacting quantum systems, leading to ambiguities in the definition of thermodynamic quantities. Applying the Schmidt basis formalism to general bipartite autonomous…
We investigate how the compositeness of a quantum system influences the characteristic time of equilibration. We study the dynamics of open composite quantum systems strongly coupled to the environment after a quantum perturbation…
This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics,…
Topology identification comprises reconstructing the interaction Hamiltonian of a quantum network by properly processing measurements of its density operator within a fixed time interval. It finds application in several quantum technology…
In this thesis, we focus on the energetic analysis within autonomous quantum systems. To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems. From the Schmidt…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…
We study a random model of deep multi-head self-attention in which the weights are resampled independently across layers and heads, as at initialization of training. Viewing depth as a time variable, the residual stream defines a…
In an earlier paper of Cadek, Vokrinek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all possible homotopy classes of maps between two topological…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
We show that the standard Hamiltonian of isotropic loop quantum cosmology is selected by physical criteria plus one choice: that it have a `minimal' number of terms. We also show the freedom, and boundedness of energy density, even when…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
A steadily growing computational power is employed to perform molecular dynamics simulations of biological macromolecules, which represents at the same time an immense opportunity and a formidable challenge. In fact, large amounts of data…
We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. This framework enables us to express an indirect…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…