A periodically driven system generally has symmetry with respect to translation in time by the drive period. Such discrete time-translation symmetry can be spontaneously broken, leading to dynamics with a period, which is a multiple of the driving period. Where this happens in many-body systems, they are said to form time crystals. In dissipative systems, the symmetry breaking can be mediated by noise. The concept will be illustrated on an example of coupled parametrically driven oscillators. Such oscillators can be cold atoms in a modulated magneto-optical trap, where the time-crystal transition has been observed, or nanomechanical oscillators or microwave cavity modes. The noise can be thermal or purely quantum, coming from the spontaneous emission of photons/phonons by a driven system. The effect is based on noise-induced transitions between coexisting period-two vibrational states, somewhat reminiscent of what is studied in stochastic resonance. The overall dynamics of the many-body system display features that have no analog in equilibrium systems, particularly in the presence of disorder.

We report on the onset of resonant and anti-resonant behaviour of mass transport systems driven by time-dependent forces. We show that cooperation between the noise and an external forces whose spectrum contains a high enough number of harmonics leads to the appearance of new resonant states of the system. The increase in the number of modes of the external force causes the system to switch from the regime of a single resonant peak, typical of the case of a small number of modes, to a regime in which a pair of resonant-antiresonant peaks arise. Forces whose spectrum consists of a high number of coupled modes required for the appearance of antiresonances arise naturally in the case of systems confined by uneven and flexible walls.

We shown this feature by analyzing the dynamics of a polymer chain confined within a channel whose walls undergo sustained oscillations. Our numerical data confirm the predictions of the analytical model and show a clear correlation between the number of modes (encoded in the variance of the Fourier power spectrum) and the onset of the antiresonant minimum. The results obtained broaden the understanding of the resonant phenomena in drift-diffusion systems and may provide the rational for the interpretation of dataset existing in the literature. The existence of the new regimes we have found, in which resonances and antiresonances coexist, opens up the possibility of designing the driving force to be able to control the flow of particles and to manipulate nano-objects in order to study their properties.

References:

F. Carusela, P. Malgaretti, J. M. Rubi, "Antiresonant driven systems for particle manipulation" PRE in press

All known forms of life rely on ion channels to enable the passage of ions across cellular membranes. The permeation mechanism involves stochastic activation over an energy barrier due in part to the membrane potential and that due to the dielectric mismatch between the channel protein and the water within it. But the reality is more complex than that, as evidenced by the fact that channels can be highly selective for particular ions. This selectivity is associated with a fixed negative charge Q_f in the narrow section of the channel known as the selectivity filter. Remarkably, many channel properties can now be interpreted [1] by analogy with the physics of quantum dots: e.g. the alternating conduction bands and stop bands seen for ions in channels as Q_f is varied correspond to Coulomb blockade oscillations in quantum dots. These are emergent phenomena that would not have been expected from known channel structure. We discuss stochastic vs. quantum comparisons, present the first systematic numerical and experimental tests of the ionic Coulomb blockade picture [2] and describe recent work developing a fundamental statistical theory [3] to describe the conduction mechanism.

[1] I. Kh. Kaufman, P. V. E. McClintock, and R. S. Eisenberg, "Coulomb blockade model of permeation and selectivity in biological ion channels", New J. Phys. 17, 083021 (2015).

[2] O. A. Fedorenko, I. Kh. Kaufman, W.A.T. Gibby, M.L. Barabash, D.G. Luchinsky, S.K. Roberts, and P.V. E. McClintock, "Coulomb blockade and the determinants of selectivity in the NaChBac bacterial sodium channel", Biochim. Biophys. Acta (BBA) 1862, 183301 (2020).

[3] W. A. T. Gibby, M. L. Barabash, C. Guardiani, D. G. Luchinsky, and P. V. E. McClintock, "Physics of selective conduction and point mutation in biological ion channels", Phys. Rev. Lett. 126, 218102 (2021).

We show the presence of stochastic resonance in the motion of Brownian particles through a deformable micro-channel when a periodic force is applied. The resonance is entropic in nature as channel shape variations limit the space available to the particles, inducing an entropic potential.

The situation analysed occurs in the transport of particles through microfluidic or protein channels. We analyse in particular the case of drug-delivery to cancerous tissues where the stochastic resonance results from the application of ultrasounds which deform the channels. We show the existence of a maximum of the distance travelled by drug-carrying nanoparticles before delivery, as observed in experiments. Our results indicate that an appropriate channel design and a suitable choice of applied forces lead to optimal scenarios for the control of particle transport.

We give an account of recent results on quantum systems relaxing to equilibrium due to the contact with a thermal reservoir (real noise) or evolving in time as classical Markov chains (virtual noise).

It is well established that the thermalization of quantum systems is taken into account, except for memory effects, by a Lindblad dynamics. In this approach, the main problem is the choice of the Lindblad operators describing the interaction system-environment. A simple, yet completely general, choice exists for systems made of noninteracting particles in contact with a blackbody radiation. By this choice one can separate the thermalization process in two dissipation and decoherence subprocesses. The result is of experimental interest and resolves the known pathologies of the popular quantum optical master equation.

The introduction of virtual noise may transform, by means of a Feynman-Kac-like formula, the evolution problem of a quantum system into a probabilistic problem involving only classical Markov chains. Applying this exact probabilistic representation at an imaginary time, to be identified with the inverse temperature, we show that an isolated quantum system may undergo a condensation phase transition. This is not a condensation of matter in the ordinary space, rather a condensation of the degrees of freedom within the amazing complex space of the quantum wavefunctions. The mechanism allows to shed full light on the elusive Wigner crystal, a phase transition proposed by Eugene Wigner in 1934 and still under investigation.

In this talk we will discuss how several concepts of stochastic thermodynamics and statistical physics can be useful for several technological applications.

We will start by showing how the Transient Fluctuation Theorem can be used to calibrate force measurements in atomic force microscopies. We will then discuss the problem of first passage time in real applications such as for example the optimal Maxwell's demon. The resetting to the origin is one of the efficient theoretical strategies that allow a Brownian particle to reach a target in an optimal time. However we will show how in realistic situation the original assumptions used in these theoretical strategies must be modified in order to optimize the searching time.

We will finally present the Engineered Swift Equilibration which is a method to switch a system from one state to another much faster than its natural equilibration time. The initial and final state can be either an equilibrium or out of equilibrium state. We will show how this technique can speed up for example the force measurements in atomic force microscopies.

Thermodynamics together with its parallel, Statistical Mechanics, in thermal equilibrium are well-established theories, as put forward by pioneers such as Gibbs, Boltzmann, Einstein and many others. However, given the recent activity in the study of the thermodynamics of small mesoscopic and nanoscopic systems those concepts as in use on the macroscopic level require anew an in depth scrutiny. An example is the role of the equivalence for different ensemble setups. In addition, concepts such as processes of *work* and *heat* need to be studied carefully when taken into the realm of nonequilibrium (e.g. for "Stochastic Thermodynamics") and becomes quite intriguing within a quantum setting, such as when studying quantum fluctuation relations and quantum heat engines. The present literature is flagged with several controversies for what the quantum nature for work and heat (together with the enigma of their fluctuations) should refer to. The objectives become truly a challenge in describing small classical and/or quantum systems that typically are interacting *strongly* with environment(s). Yet another principal difficulty comprises the notorious invasive character of quantum measurements, i.e. the role of quantum back-action, together with the non-commutative property of corresponding observables at varying instants of time [5].

An overview of the present state of the art is presented, including in pointing to a plethora of subtleties, pitfalls and inconsistencies, ill-defined concepts and *still open issues*, occurring in classical and quantum settings. Even at manifest thermal equilibrium, these thermodynamic notions become surprisingly tricky. Hence, in distinct contrast to what one might hypothesize: - If anything can be said at all - it should be stated most clearly (Ludwig Wittgenstein, 1889-1951).

Reference: P. Talkner and P. Hänggi, Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical, Rev. Mod. Phys. 92, 041002 (2020)

In the original SR studies of 1981-1982, a weak low-frequency signal acting on a bistable system in presence of weak noise led to a large output signal due to strong modulation of the transition rates. However modulation of the activation barriers, adiabatically following the instantaneous potential barriers, was small. We now report a stronger phenomenon where a weak drive at an appropriate frequency decreases the activation barriers much more than the maximum decrease by adiabatic driving at the same amplitude: the decrease in activation barrier can be comparable to the original barrier height even though the drive amplitude is small. The effect might be used e.g. for the efficient control of memory cells.

Relevant undriven models are underdamped stochastic systems possessing 2 or more saddles: such models are valid e.g. for some NEMS/MEMS, ac SQUIDs, optically levitated nanoparticles, and ferromagnets. The mechanism is a strong resonant action of the drive over a broad energy range, its strength being due to the presence of more than 1 saddle.

To illustrate the idea, we have studied a characteristic model finding e.g. that, if the adiabatic drive provides a maximum decrease in activation barrier of 1.24%, then a drive of the same amplitude and appropriate frequency decreases it by 51%, i.e. an effect 41 times stronger. It means that, for realistic temperatures, this tiny drive increases the transition rate by a factor of up to 10^8.

Statistics of the transition paths manifests new features. Types of statistics known hitherto were: 1D diffusion, 1D optimal paths, and their mutul combinations with or without random wandering through regions of transient chaos or chaotic saddles. In our case, new kinds of statistics appear. Their common feature is a large 2D area where the paths are distributed continuously, with their relevant parts following noise-free resonant trajectories.

The talk aims to stimulate other researchers to further develop this exciting new topic.

Most popular statistical models in epidemic evolution focus on the dynamics of average relevant quantities and overlooks the role of small fluctuations on the model parameters. Models for Covid-19 are no exception. In this paper we show that the role of time-correlated fluctuations, far from being negligible, can in fact determine the spreading of an epidemic and, most importantly, the resurgence of the exponential diffusion in the presence of time-limited episodes in promiscuity behaviours. The results found in this work are not only relevant and specific for the Covid-19 epidemic but are more general and can be applied to other epidemics.

Quantitative characterization of plasticity, robustness, and evolvability is one of the most important issues in biology. Here I review how stochasticity is relevant to spontaneous adaptation and robustness in evolution. First, it is shown that cells can make general, spontaneous adaptations, by taking advantage of stochasticity and homeostasis to compensate the growth-dilution. Second, relationship between phenotypic evolution and variances is formulated by borrowing fluctuation-relationship in statistical physice, where dimensional reduction to achieve the robustness in high-dimensional phenotypic changes is shown to be essential. These theoretical studies are verified by adaptation and evolution experiments of bacteria.

References

[1]Kaneko K., Life: An Introduction to Complex Systems Biology, Springer (2006)

[2]K. Sato, Y,Ito, T.Yomo, K. Kaneko, "On the Relation between Fluctuation and Response in Biological Systems" Proc. Nat. Acad. Sci. USA 100 (2003) 14086-14090

[3] Kashiwagi, A., Urabe, I., Kaneko, K., & Yomo, T. (2006). Adaptive response of a gene network to environmental changes by fitness-induced attractor selection. PloS one, 1, e49.

[4] K. Kaneko, "Evolution of Robustness to Noise and Mutation in Gene Expression Dynamics" PLoS One(2007) 2 e434

[5]K. Kaneko, C.Furusawa, T. Yomo, "Macroscopic phenomenology for cells in steady-growth state", Phys.Rev.X(2015) 011014

[6] C. Furusawa, K. Kaneko "Formation of dominant mode by evolution in biological systems". Physical Review E, 97(2018) 042410

Brownian escape is key to a wealth of physico-chemical processes, including polymer folding and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show theoretically and experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates, in breach of the intuition relying on the above scaling law, and address the corresponding conditions for maximum speed-up.

The organization known as GISAID started as an initiative to store and share all influenza data. Since the start of the COVID19 pandemic it has become the main repository of SARS-CoV-2 genome sequences. As of writing this abstract (July 13, 2021) there are more than 2,300,000 SARS-CoV-2 submissions on GISAID, many of them whole-genome sequences labelled as high quality. This makes GISAID one of the largest, richest and most easily accessible data sources in all genomics.

I will discuss some simple analysis that can be done with such data, likely a harbinger of many similar data resources to appear in the future.

First, one can compute time series of frequencies of mutations. Such time series graphically for instance demonstrate that the variant now known as "beta" (B.1.351) is in fact the agglomeration of different variants.

Second, the distribution of coronaviruses over genotypes is shaped by evolution, a process driven by natural selection, mutations, genetic drift (finite-N noise) and recombination. Coronoviruses are in general known to have significant recombination, and there are reports of ongoing recombination in SARS-CoV-2 in human hosts. It was discovered by Motoo Kimura in the mid-60ies that if recombination is the fastest mechanism, the stationary distribution over genotypes is of the Ising/Potts type from equilibrium statistical mechanics. One can hence apply simple machine learning techniques to infer parameters of such distributions from sequence data, and check how stable are those parameters.

GISAID data is hence also an avenue to explore the dynamic origin of Gibbs-Boltzmann distributions (or max-entropy distributions) in biological systems that do not satisfy detailed balance, a now widely used data analysis technique alternatively called Direct Coupling Analysis (DCA) or Inverse Ising/Potts problems.

In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows us to understand the causal relations between the variables of a multidimensional linear Markov process. It is shown that the fluctuation-response formalism can be used both to find the direct causal links between the variables of a system and to introduce a degree of causation, cumulative in time, whose physical interpretation is straightforward. Although for generic nonlinear dynamics there is no simple exact relationship between correlations and response functions, the described protocol can still give a useful proxy also in the presence of weak nonlinear terms. This approach can be used for a critical analysis of paleoclimate data.

The discovery that biological and solid-state nanoscale pores can be employed as molecular sensors has triggered great interest and stimulated the research focused on the development of "nano-sensing" devices.

The operational performance of such devices depends on the possibility to control the rates at which the molecules to be analyzed (analytes) cross the nanopores.

This issue becomes a bottleneck when nanopores are supposed to work as high-throughput sequencing tools for large biopolymers (DNA and proteins).

In this context, we will discuss how the transport of a protein across a nanopore can be controlled at a molecular level by applying a vibration to the nanopore structure. The problem is studied using a phenomenological coarse-grained computational model of the protein chain and pore geometry.

We investigate, via molecular dynamics, the interplay between transport and protein unfolding when the section of the nanopore oscillates periodically in time, with a certain frequency (Radial Breathing Mode).

We find that when the protein is mechanically pulled into the vibrating nanopore it exhibits translocation dynamics which in some frequency range is accelerated, also showing a frequency locking to the pore dynamics.

The pore oscillation is able to suppress stalling events in the translocation dynamics, hence, proper frequency tuning allows both regularization and control of the overall transport process.

Finally, the interpretation of the simulation results is easily achieved by resorting to a first passage theory of elementary driven-diffusion processes.

Nonlinear dynamical systems are abundant in natural and technological systems, ranging from all branches of physical sciences to engineering as well as life sciences to medicine. Their dynamics and applications have been extensively investigated from multidisciplinary point of view. When driven by dual frequency external excitations, nonlinear systems can exhibit plethora of properties - one of the most prominent being resonance. Depending on the nature of the driving force, whether of stochastic or deterministic origin, the resonance phenomenon could, in general, be termed stochastic resonance (SR) or vibrational resonance (VR) which were first reported about 40 years and 20 years ago, respectively. The theories, methods of analysis, associated mechanisms and applications in modern advanced technologies of these two phenomena are also closely related. This paper will provide a concrete up-to-date overview of stochastic and/or high-frequency periodic excitation- induced resonances in driven systems. It will focus on and address some significant state-of-the-art results on specific applications related to the design of machines and devices that exert vibrations on materials, the improvement of image quality, the construction of logic gates, the harvesting of energy from various forms of ambient vibrations, the control of aerodynamics vibration-induced instabilities, improvement of all-optical switching for applications in communication systems and enhancement of autodyne signals in self-mixing optical interferometry. The paper will, in addition, highlight some possible new research directions on SR and VR.

In this talk, I will shortly reviewed how stochastic resonance was discovered. In particular I will focus on the difficulties in applying the original idea in climate changes. Among others, I will discuss the physical concept of equilibrium and noise and their meanings in the climate problem.

A generic one variable model giving rise to three stable steady-states is considered. In the presence of Gaussian white noise, provided that certain conditions are fulfilled, Kramers' theory predicts random transitions across the potential barriers between states. In this framework the classical setting of stochastic resonance is extended to account for the presence of an additional periodic forcing. General expressions of the linear response of the system are derived and the role of the parameters on the probabilistic long term dynamics is highlighted.

Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to the divergence of all the moments (cumulants). We have solved this problem by introducing a pseudo-cumulants’ expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsinc and endogenous fluctuations, thus obtaining an unified mean-field formulation encompassing quenched and dynamical disorder sources.

For macroscopic systems, the second law of thermodynamics unambiguously determines the direction of the arrow of time: the arrow points toward increasing entropy. In microscopic systems, thermal noise is prevalent and may lead to so-called violations of the second law, making it difficult to determine with accuracy the direction of time's arrow. I will discuss theoretical work that quantifies our ability to identify the direction of time's arrow, leading to a testable prediction, and I will show experimental data verifying this prediction. I will also present recent results in which neural networks were trained, using supervised learning, to distinguish between forward-in-time and backward-in-time trajectories. Remarkably, even though this training involved no more than presenting the networks with a set of labelled ("forward" / "backward") trajectories, the networks spontaneously learned that entropy production is the key feature in determining the direction of time's arrow.

It has been observed that patients with neurodegenerative diseases, such as Alzheimer, Parkinson and Huntington's disorders, accumulate metals (primarily iron) in the basal ganglia of their brains. In this context several techniques have been exploited to measure brain iron levels, these include Positron Emission Tomography (PET), Magnetic Resonance Imaging (MRI) and measurement systems based on magnetic sensors (i.e. SQUID magnetometers). All these techniques have their advantages and disadvantages, cost and complexity of equipment being one of the primary disadvantages. Hence, these techniques are usually not applied for diagnostics, until the patient actually starts to show signs of the neural degeneration; at this point there is, at present, no treatment except simply monitoring the disease and providing "quality-of-life" care. The Advanced Dynamic Magnetometer affords an alternative low cost solution for quantifying brain iron content. The device operation is underpinned by a neuromorphic "rate code" that allows an extremely simple and noise-tolerant readout, while allowing measurements to be carried out in a medical clinic setting, at room temperature. In this talk we review the operating principle of the magnetometer and discuss figures of merit (e.g. SNR, Resolution) that quantify its performance in the presence of a noise-floor. We show the results of laboratory experiments carried out using a newly engineered version of the magnetometer, with a mockup of the human skull having ferrofluid implants to simulate different iron concentrations. Finally, we show the first (admittedly raw) results of measurements carried out on human subjects. The results show that if a baseline for comparison can be established, then there is the potential to measure the brain iron of elderly patients as part of a routine medical checkup; done at regular intervals, this might catch the onset of the neural degeneration at an early stage.

For a physicist, even after a quick look, the brain offers an exuberance of phenomenology which can be rigorously related with two concepts that occupy statistical physicists for the last few decades: critical phenomena and stochastic resonance (SR). I been very fortunate to be, by chance, at the cross roads of these two concepts, thus I will make my best to review our own contributions following Frank Moss and colleagues insistence on SR on one side, and on the other to our work which originates in Per Bak's enthusiasm for studying brain dynamics as another critical phenomena.

The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment (e.g. an aqueous solution), thus keeping them permanently out of equilibrium. Nevertheless, the spatial dynamics of active particles might share certain equilibrium features, in particular in the steady state. We here focus on the time-reversal symmetry of individual spatial trajectories as a distinct equilibrium characteristic.

Within the framework of active Ornstein–Uhlenbeck particles we calculate the log-ratio of path probabilities for observing a certain particle trajectory forward in time versus observing its time-reserved twin trajectory, and derive a generalized "entropy production", which fulfills an integral fluctuation theorem. Using this "entropy production" we then investigate to what extent the steady-state trajectories of a trapped active particle obey or break time-reversal symmetry. We find that the steady-state trajectories in a harmonic potential fulfill path-wise time-reversal symmetry exactly, while this symmetry is typically broken in anharmonic potentials.