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Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly…
We develop the thermodynamics of non-Markovian generalized Langevin equations by embedding them in a high-dimensional Markovian representation involving auxiliary degrees of freedom. If the memory is linear and satisfies detailed balance…
Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects…
In classical physics, memoryless dynamics and Markovian statistics are one and the same. This is not true for quantum dynamics, first and foremost because quantum measurements are invasive. Going beyond measurement invasiveness, here we…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
Markovian master equations provide a versatile tool for describing open quantum systems when memory effects of the environment may be neglected. As these equations are of an approximate nature, they often do not respect the laws of…
In the paradigm of thermodynamic computing, instead of behaving deterministically, hardware undergoes a stochastic process in order to sample from a distribution of interest. While it has been hypothesized that thermodynamic computers may…
The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…
A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…
We establish a connection between non-Markovian memory effects and thermodynamical quantities such as work. We show how memory effects can be interpreted as revivals of work that can be extracted from a quantum system. We prove that…
Interest in the thermodynamics of computation has revived in recent years, driven by developments in science, economics and technology. Given the consequences of the growing demand for computational power, the idea of reducing the energy…
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle…
The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital…
Non-Markovian dynamics arise when a system is coupled to a bath with finite correlation time, giving rise to memory effects that allow the bath to temporarily store and return excitations. However, how memory modifies irreversibility and…
Stochastic thermodynamics investigates energetic and entropic bounds in small systems. Foundational results, e.g., the first and second laws, predominantly rely on the Markov (memoryless) assumption. Although physicists recognise that the…
The emergence of irreversibility in physical processes, despite the fundamentally reversible nature of quantum mechanics, remains an open question in physics. This thesis explores the intricate relationship between quantum mechanics and…
We speculate whether the second law of thermodynamics has more to do with Turing machines than steam pipes. It states the logical reversibility of reality as a computation, i.e., the fact that no information is forgotten: nature computes…
Quantum Markov models are employed ubiquitously in quantum physics and in quantum information theory due to their relative simplicity and analytical tractability. In particular, these models are known to give accurate approximations for a…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…