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Thermodynamic uncertainty relations (TURs) impose a universal trade-off between current precision and entropy production in autonomous steady states, constraining in particular the power, efficiency, and constancy of heat engines. We…

We model the well-known interlinked cascade of Rab GTPases found in eukaryotic cells by using a network of Markov states to investigate the universal Thermodynamic Uncertainty Relation for the non-equilibrium system. First, we prove…

Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.

We consider a stochastic model described by two stochastic differential equations of motion; one is for the stochastic evolution forward in time and the other for backward in time. We further introduce averaged quantities for the two…

We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval $t$. A heat, which differs from a work by an energy change, is shown to…

It is shown that the conclusion [arXiv:1208.1166v2] made by Porsch and R\"oseler that their cutoff polaron theory transforms to Tulub theory is erroneous. The results of the work by Klimin and Devreese based on the results of Porsch and…

Time-energy uncertainty relation (TEUR) plays a fundamental role in quantum mechanics, as it allows to grasp peculiar aspects of a variety of phenomena based on very general principles and symmetries of the theory. Using the Mandelstam-Tamm…

We review the trade-offs between speed, fluctuations, and thermodynamic cost involved with biological processes in nonequilibrium states, and discuss how optimal these processes are in light of the universal bound set by the thermodynamic…

We investigate the statistical properties of fluctuations in active systems that are governed by non-symmetric responses. Both an underdamped Langevin system with an odd resistance tensor and an overdamped Langevin system with an odd…

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,…

I examine the arguments which have been given for quantum fluctuation-dissipation theorems. I distinguish between a weak form of the theorem, which is true under rather general conditions, and a strong form which requires a Langevin…

We consider a localized quantum system living in a curved spacetimes. By translating into this scenario the paradgmatic two-point measument scheme in quantum statistical mechanics we are able to prove a relativistic version of the quantum…

In this contribution, the estimates for the response of time delay systems with nonlinear homogeneous right-hand side of degree strictly greater than one are constructed. The existing results obtained via the Lyapunov--Razumikhin approach…

Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in 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…

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…

Thermodynamic uncertainty relations (TURs) relate precision to the dissipation rate, yet the inequalities can be far from saturation. Indeed, in catenane molecular motor simulations, we record precision far below the TUR limit. We further…

Nanoscale heat engines are subject to large fluctuations which affect their precision. The Thermodynamic Uncertainty Relation (TUR) provides a trade-off between output power, fluctuations and entropic cost. This trade-off may be overcome by…

The widely used linear-response (LR) theory of thermal conduction in the quantum regime rests on the yet unproven assumption, that the thermal conductivity is invariant with respect to the gauge of the energy density of the system. This…

We study the implications of translation invariance on the tangent dynamics of extended dynamical systems, within a random matrix approximation. In a model system, we show the existence of hydrodynamic modes in the slowly growing part of…