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Temperature uncertainty of a quantum system in canonical ensemble is inversely determined by its energy fluctuation, which is known as the temperature-energy uncertainty relation. No such uncertainty relation was discovered for a…
Thermodynamic Uncertainty Relations (TURs) are relations that establish lower bounds for the relative fluctuations of thermodynamic quantities in terms of the statistics of the associated entropy production. In this work we derive a family…
Fluctuation relations are identities, holding in non-equilibrium systems, that have attracted a lot of interest in the last 20 years. This is a series of 4 lectures discussing various aspects of such relations for stochastic equations…
The fluctuation-dissipation relation tells that dissipation always accompanies with thermal fluctuations. Relativistic fluctuating hydrodynamics is used to study the effects of the thermal fluctuations in the hydrodynamic expansion of the…
We study analytically the probability distribution of the heat released by an ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium relaxation process following a temperature quench. We focus on the asymmetry…
We use dynamic equations to derive a relation between correlation functions and response or relaxation functions in many-body systems. The relation is very general and holds both in equilibrium, when the usual fluctuation-dissipation…
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…
Small systems in contact with a heat bath evolve by stochastic dynamics. Here we show that, when one such small system is weakly coupled to another one, it is possible to infer the presence of such weak coupling by observing the violation…
This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of…
Continuing our inquiry into the conditions when fluctuation-dissipation relations (FDR) may appear in the context of nonequilibrium dynamics of open quantum systems (over and beyond the conventional FDR from linear response theory) we turn…
Entropy and the fluctuation-dissipation theorem are at the heart of statistical mechanics near equilibrium. Driving a system beyond the linear response regime leads to (i) the breakdown of the fluctuation-dissipation theorem and (ii) a…
We consider heat fluctuations and fluctuation theorems for systems driven by multiple reservoirs. We establish a fundamental symmetry obeyed by the joint probability distribution for the heat transfers and system coordinates. The symmetry…
Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for…
The fluctuation relations have received considerable attention since their emergence and development in the 1990s. We present a summary of the main results and suggest ways to interpret this material. Starting with a consideration of the…
Fluctuation theorems impose constraints on the probability of observing negative entropy production in small systems driven out of equilibrium. The range of validity of fluctuation theorems has been extensively tested for transitions…
We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal)…
In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by…
There is no simple fluctuation-dissipation theorem (FDT) for nonequilibrium systems. We show that for a fluid in a nonequilibrium steady state (NESS) characterized by a constant temperature gradient there is a generalized FDT that relates…
As a fundamental measure of stability in nonequilibrium thermodynamics, fluctuations provide critical insight into the performance and reliability of heat engines. In this work, we establish universal fluctuation-dissipation bounds that…
Thermal fluctuations in non-equilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these…