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Many versions of Thermodynamic Uncertainty Relations (TUR) have recently been discovered, which impose lower bounds on relative fluctuations of integrated currents in irreversible dissipative processes, and suggest that there may be…
The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian…
The uncertainty principle is a cornerstone of modern physics, and its implications have a fundamental impact on theoretical and applied quantum mechanics. The aim of this thesis is to study and apply the uncertainty relations between time…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
We investigate the thermodynamic uncertainty relations (TURs) in steady-state transport for a multi-terminal system consisting of two conducting terminals and N-2 probe terminals, within the linear response regime under broken time-reversal…
It is shown that the well-defined unbiased measurement or disturbance of a dynamical variable is not maintained for the precise measurement of the conjugate variable, independently of uncertainty relations. The conditionally valid…
Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
We generalize thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs). The scaled diffusion coefficient derived by considering the connection between macroscopic CRNs…
We present a new uncertainty relation by defining a measure of uncertainty based on skew information. For bipartite systems, we establish uncertainty relations with the existence of a quantum memory. A general relation between quantum…
Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to an ad-hoc operating point,…
The uncertainty principle bounds our ability to simultaneously predict two incompatible observables of a quantum particle. Assisted by a quantum memory to store the particle, this uncertainty could be reduced and quantified by a new…
The generalized uncertainty connection between the fluctuations of a quantum observable and its temporal derivative is derived in this study, we demonstrate that the product of an observable's uncertainties and its time derivative is…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
Entropy production plays an important role in the regulation and stability of active matter systems, and its rate quantifies the nonequilibrium nature of these systems. However, entropy production is hard to be experimentally estimated even…
We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the…
Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this Letter, we explore this…
The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
In classical Markov jump processes, current fluctuations can only be reduced at the cost of increased dissipation. To explore how quantum effects influence this trade-off, we analyze the uncertainty of steady-state currents in Markovian…