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Non-equilibrium Fluctuations and Cooperativity in Single-Molecule Dynamics: Going Beyond Fluctuation Theorems and Large Deviation Theory: Thermodynamically consistent renewal networks for driven single-molecule dynamics with memory

Applicant Dr. Aljaz Godec
Subject Area Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Term from 2017 to 2022
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 316896626
 
Final Report Year 2023

Final Report Abstract

Single-molecule experiments probe processes on the level of individual trajectories during relaxation or in stationary states. Observations are typically analyzed by averaging along individual realizations yielding fluctuating quantities with nontrivial statistics. Such time-averaged observables, in particular generalized currents, are central to Stochastic Thermodynamics. Low dimensional projections underlying single-molecule observations (e.g. force spectroscopy, FRET, and plasmon ruler experiments) leave behind hidden degrees of freedom, often evolving as slowly as the observable. It is long known that projections that hide slow degrees of freedom lead to memory. However, it only recently became clear that projections raise great challenges in the formulation and understanding of stochastic thermodynamics of systems with slow hidden degrees of freedom, especially when these are driven far from equilibrium. Similarly, the kinetics of binding and chemical reactions in the limit of high dilution (i.e. involving ∼ 1−100 molecules) are subject to large fluctuations with non-Poissonian statistics. Whereas theoretical studies so far focused on predicting kinetics for specific models via the statistics of the first-passage time, practical applications typically aim at inferring kinetic rates–inverse mean first-passage times– from experiments or simulations. Such inference is challenging because usually only a small number of realizations (1 − 10, occasionally up to 100) are available. This gives rise to large uncertainties and non-Gaussian errors, which are especially detrimental in the case of broadly distributed and high-dimensional data. The project focused on a (i) general theory of time-average statistical mechanics, (ii) the thermodynamics of non-equilibrium systems observed via low dimensional projections, and (iii) sampleto-sample fluctuations in statistical kinetics. We achieved important progress in all listed topics. In particular, (i) we developed a general approach to time-average statistical mechanics using stochastic calculus, unveiling a fundamental threefold need for spatial coarse-graining and delivering a direct proof of the celebrated Thermodynamic Uncertainty Relation and conditions for its saturation. Moreover, (ii) we discovered the phenomenon of kinetic hysteresis – the non-commutability of coarse graining and time-reversal – important for understanding and quantifying irreversibility in the presence of memory, and established milestoning – a coarse-graining method that disregards parts of the configuration space – as a thermodynamically consistent reduction method. Furthermore, (iii) we developed a general framework for determining complete first-passage statistics with important applications in extreme value theory, as well as a theory enabling the control of uncertainty of first-passage times inferred from under-sampled data. In addition to these planned topics, we discovered an unforeseen asymmetry between heating and cooling, that is, that heating in fact quite generally occurs faster than cooling, and investigated collective phenomena in strongly-interacting many-body systems, where we uncovered a novel kind of dynamical phase transition in kinetic spin systems and developed an explicit phase field theory of interfacial phenomena that accounts for correlations between particles.

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