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In nonequilibrium steady states of Markov jump processes, we derive exact Fluctuation-Response Relations (FRRs) that express the covariance between any pair of currents in terms of static responses in a notably simple form, thus…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a trade-off relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines.…
We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple…
Discrete-time counterpart of thermodynamic uncertainty relation (conjectured in P. Pietzonka, et.al., arXiv:1702.07699 (2017)) with finite time interval is considered. We show that this relation do not hold by constructing a concrete…
Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical…
For processes during which a macroscopic system exchanges no heat with its surroundings, the second law of thermodynamics places two lower bounds on the amount of work performed on the system: a weak bound, expressed in terms of a…
Thermodynamic uncertainty relations (TURs) are recently established relations between the relative uncertainty of time-integrated currents and entropy production in nonequilibrium systems. For small perturbations away from equilibrium,…
We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…
We investigate transient version of the recently discovered thermodynamic uncertainty relation (TUR) which provides a precision-cost trade-off relation for certain out-of-equilibrium thermodynamic observables in terms of net entropy…
The uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the paper by two of the present…
We derive a condition for the realizability of heat released in nondeterministic processes from a fluctuation theorem, showing that this condition is strictly stronger than the probabilistic form of the second law of thermodynamics. With…
A fluctuation relation for the heat exchange of an open quantum system under a thermalizing Markovian dynamics is derived. We show that the probability of that the system absorbs an amount of heat from its bath, at a given time interval,…
We derive detailed and intergral fluctuation relations as well as a Thermodynamic Uncertainty Relation constraining the exchange statistics of an arbitrary number of non-commuting conserved quantities among two quantum systems in transport…
Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At the microscale, another distinct possibility becomes more likely: processes in which no entropy is…
The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is…
We derive an uncertainty relation for the energy density and pressure of a quantum scalar field in a time-dependent, homogeneous and isotropic, classical background, which implies the existence of large fluctuations comparable to their…
We discuss an extension of the fluctuation theorem to stochastic models that, in the limit of zero external drive, are not able to equilibrate with their environment, extending results presented by Sellitto (cond-mat/9809186). We show that…
We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic dissipation; and the analysis of…
Thermodynamic uncertainty relations (TURs) set fundamental bounds on the fluctuation and dissipation of stochastic systems. Here, we examine these bounds, in experiment and theory, by exploring the entire phase space of a cyclic information…