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The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for…

We prove a general inequality between the charge current and its fluctuations valid for any non-interacting coherent electronic conductor and for any stationary out-of-equilibrium condition, thereby going beyond established…

A generalized fluctuation-response relation is found for thermal systems driven out of equilibrium. Its derivation is independent of many details of the dynamics, which is only required to be first-order. The result gives a correction to…

A cost-precision trade-off relationship, the so-called thermodynamic uncertainty relation (TUR), has been recently discovered in stochastic thermodynamics. It bounds certain thermodynamic observables in terms of the associated entropy…

A universal large $\mathcal{N}$ theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse grained thermodynamic uncertainty relations (TUR) -- one of…

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…

It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the lower limit of inverse temperature

We use the quantum Brownian model to derive the uncertainty relation for a quantum open system. We examine how the fluctuations of a quantum system evolve after it is brought in contact with a heat bath at finite temperature. We study the…

Based on the recently proposed framework of general relativistic stochastic mechanics [{\em J. Stat. Phys.}, 190:193, 2023; {\em J. Stat. Phys.}, 190:181, 2023] and stochastic thermodynamics [{\em SciPost Physics Core} 7, 082, 2024] at the…

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…

The fluctuation-dissipation-theorem connects equilibrium to mildly (linearly) perturbed situations in a thermodynamic manner: It involves the observable of interest and the entropy production caused by the perturbation. We derive a relation…

We derive bounds to the thermodynamic uncertainty relations in the linear-response regime for steady-state transport in two-terminal systems when time reversal symmetry is broken. We find that such bounds are different for charge and heat…

In nonequilibrium systems, the relative fluctuation of a current has a universal trade-off relation with the entropy production, called the thermodynamic uncertainty relation (TUR). For systems with broken time reversal symmetry, its…

We derive a universal thermodynamic uncertainty relation for Fermionic coherent transport, which bounds the total rate of entropy production in terms of the mean and fluctuations of a single particle current. This bound holds for any…

Thermodynamic uncertainty relations elucidate the intricate balance between the precision of current and the thermodynamic costs or dissipation, marking a recent and enthralling advancement at the confluence of statistical mechanics,…

We give a novel derivation of Holevo's bound using an important result from nonequilibrium statistical physics, the fluctuation theorem. To do so we develop a general formalism of quantum fluctuation theorems for two-time measurements,…

We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three…

Recently, some general relations have been studied in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a universal internal relation among the cumulants of currents and the entropy…

Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…

We introduce ``local uncertainty relations'' in thermal many-body systems, from which fundamental bounds in quantum systems can be derived. These lead to universal non-relativistic speed limits (independent of interaction range) and…