Thermodynamic uncertainty relation bounds the extent of anomalous diffusion

In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models

Violation of Local Detailed Balance Despite a Clear Time-Scale Separation

Integrating out fast degrees of freedom is known to yield, to a good approximation, memory-less, i.e. Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee thermodynamic consistency arbitrarily far from equilibrium. Here we present a transparent example of a Markov model of a molecular motor where local detailed balance can be violated despite a clear time-scale separation and hence Markovian dynamics. Driving the system far from equilibrium can lead to a violation of local detailed balance against the driving force. We further show that local detailed balance can be restored, even in the presence of memory, if the coarse-graining is carried out as Milestoning. Our work establishes Milestoning not only as a kinetically but for the first time also as a thermodynamically consistent coarse-graining method. Our results are relevant as soon as individual transition paths are appreciable or can be resolved

Second law, entropy production, and reversibility in thermodynamics of information

We present a pedagogical review of the fundamental concepts in thermodynamics of information, by focusing on the second law of thermodynamics and the entropy production. Especially, we discuss the relationship among thermodynamic reversibility, logical reversibility, and heat emission in the context of the Landauer principle and clarify that these three concepts are fundamentally distinct to each other. We also discuss thermodynamics of measurement and feedback control by Maxwell's demon. We clarify that the demon and the second law are indeed consistent in the measurement and the feedback processes individually, by including the mutual information to the entropy production.Comment: 43 pages, 10 figures. As a chapter of: G. Snider et al. (eds.), "Energy Limits in Computation: A Review of Landauer's Principle, Theory and Experiments

Spectral theory of fluctuations in time-average statistical mechanics of reversible and driven systems

We present a spectral-theoretic approach to time-average statistical mechanics for general, nonequilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic stochastic dynamics with continuous or discrete state-space. We derive exact results for the mean, fluctuations, and correlations of time-average observables from the eigenspectrum of the underlying generator of Fokker-Planck or master equation dynamics, and we discuss the results from a physical perspective. Feynman-Kac formulas are rederived using Itô calculus and combined with non-Hermitian perturbation theory. The emergence of the universal central limit law in a spectral representation is shown explicitly on large-deviation timescales. For reversible dynamics with equilibrated initial conditions, we derive a general upper bound to fluctuations of occupation measures in terms of an integral of the return probability. Simple, exactly solvable examples are analyzed to demonstrate how to apply the theory. As a biophysical example, we revisit the Berg-Purcell problem on the precision of concentration measurements by a single receptor. Our results are directly applicable to a diverse range of phenomena underpinned by time-average observables and additive functionals in physical, chemical, biological, and economical systems