The essence of phase transitions in condensed matter by an information theoretic approach.

Our information theoretic considerations suggest that the essence of phase transitions in condensed matter is the change in entropy as reflected in the change in the number of isomers between two phases. The explicit number of isomers as a function of size is computed using a graph theoretic approach that is compared to a direct count for smaller systems. This allows us to apply a common approach to both nanosystems and their macroscopic limit. The entropy increases very rapidly with size with the results that replacing the actual distribution over size by an average is not an accurate approximation. That the phase transition is a sharp function of the temperature is due to the high heat capacity of both the solid and liquid phases. The difference in entropy at the transition is related to the Trouton-Richards considerations. The finite width of the boundary between two phases of a finite system is related to the inherent uncertainty product that is derived from the maximum entropy formalism and that is a result of the fluctuations about equilibrium. As the system size increases, the boundary becomes sharper and one recovers the usual thermodynamic description.

A quantum information processing machine for computing by observables.

A quantum machine that accepts an input and processes it in parallel is described. The logic variables of the machine are not wavefunctions (qubits) but observables (i.e., operators) and its operation is described in the Heisenberg picture. The active core is a solid-state assembly of small nanosized colloidal quantum dots (QDs) or dimers of dots. The size dispersion of the QDs that causes fluctuations in their discrete electronic energies is a limiting factor. The input to the machine is provided by a train of very brief laser pulses, at least four in number. The coherent band width of each ultrashort pulse needs to span at least several and preferably all the single electron excited states of the dots. The spectrum of the QD assembly is measured as a function of the time delays between the input laser pulses. The dependence of the spectrum on the time delays can be Fourier transformed to a frequency spectrum. This spectrum of a finite range in time is made up of discrete pixels. These are the visible, raw, basic logic variables. The spectrum is analyzed to determine a possibly smaller number of principal components. A Lie-algebraic point of view is used to explore the use of the machine to emulate the dynamics of other quantum systems. An explicit example demonstrates the considerable quantum advantage of our scheme.

Nonadiabatic quantum dynamics explores non-monotonic photodissociation branching of N2 into the N(4S) + N(2D) and N(4S) + N(2P) product channels.

Vacuum ultraviolet (VUV) photodissociation of N2 molecules is a source of reactive N atoms in the interstellar medium. In the energy range of VUV optical excitation of N2, the N-N triple bond cleavage leads to three types of atoms: ground-state N(4S) and excited-state N(2P) and N(2D). The latter is the highest reactive and it is believed to be the primary participant in reactions with hydrocarbons in Titan's atmosphere. Experimental studies have observed a non-monotonic energy dependence and non-statistical character of the photodissociation of N2. This implies different dissociation pathways and final atomic products for different wavelength regions in the sunlight spectrum. We here apply ab initio quantum chemical and nonadiabatic quantum dynamical techniques to follow the path of an electronic state from the excitation of a particular singlet 1Σ+u and 1Πu vibronic level of N2 to its dissociation into different atomic products. We simulate dynamics for two isotopomers of the nitrogen molecule, 14N2 and 14N15N for which experimental data on the branching are available. Our computations capture the non-monotonic energy dependence of the photodissociation branching ratios in the energy range 108 000-116 000 cm-1. Tracing the quantum dynamics in a bunch of electronic states enables us to identify the key components that determine the efficacy of singlet to triplet population transfer and therefore predissociation lifetimes and branching ratios for different energy regions.

Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size.

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N2 logic variables per N level system. This is how massive parallelism is achieved in that there are N2 potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N2 expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.

Thermodynamic energetics underlying genomic instability and whole-genome doubling in cancer.

Genomic instability contributes to tumorigenesis through the amplification and deletion of cancer driver genes. DNA copy number (CN) profiling of ensembles of tumors allows a thermodynamic analysis of the profile for each tumor. The free energy of the distribution of CNs is found to be a monotonically increasing function of the average chromosomal ploidy. The dependence is universal across several cancer types. Surprisal analysis distinguishes two main known subgroups: tumors with cells that have or have not undergone whole-genome duplication (WGD). The analysis uncovers that CN states having a narrower distribution are energetically more favorable toward the WGD transition. Surprisal analysis also determines the deviations from a fully stable-state distribution. These deviations reflect constraints imposed by tumor fitness selection pressures. The results point to CN changes that are more common in high-ploidy tumors and thus support altered selection pressures upon WGD.

Time evolution of entanglement of electrons and nuclei and partial traces in ultrafast photochemistry.

Broad in energy optical pulses induce ultrafast molecular dynamics where nuclear degrees of freedom are entangled with electronic ones. We discuss a matrix representation of wave functions of such entangled systems. Singular Value Decomposition (SVD) of this matrix provides a representation as a sum of separable terms. Their weights can be arranged in decreasing order. The representation provided by the SVD is equivalent to a Schmidt decomposition. If there is only one term or if one term is already a good approximation, the system is not entangled. The SVD also provides either an exact or a few term approximation for the partial traces. A simple example, the dynamics of LiH upon ultrafast excitation to several non-adiabatically coupled electronic states, is provided. The major contribution to the entanglement is created during the exit from the Franck Condon region. An additional contribution is the entanglement due to the nuclear motion induced non-adiabatic transitions.

Intracellular redox potential is correlated with miRNA expression in MCF7 cells under hypoxic conditions.

Hypoxia is a ubiquitous feature of cancers, encouraging glycolytic metabolism, proliferation, and resistance to therapy. Nonetheless, hypoxia is a poorly defined term with confounding features described in the literature. Redox biology provides an important link between the external cellular microenvironment and the cell's response to changing oxygen pressures. In this paper, we demonstrate a correlation between intracellular redox potential (measured using optical nanosensors) and the concentrations of microRNAs (miRNAs) involved in the cell's response to changes in oxygen pressure. The correlations were established using surprisal analysis (an approach derived from thermodynamics and information theory). We found that measured redox potential changes reflect changes in the free energy computed by surprisal analysis of miRNAs. Furthermore, surprisal analysis identified groups of miRNAs, functionally related to changes in proliferation and metastatic potential that played the most significant role in the cell's response to changing oxygen pressure.

Consecutive feedback-driven constitutional dynamic networks.

Cellular transformations are driven by environmentally triggered complex dynamic networks, which include signal-triggered feedback processes, cascaded reactions, and switchable transformations. We apply the structural and functional information encoded in the sequences of nucleic acids to construct signal-triggered constitutional dynamic networks (CDNs) that mimic the functions of natural networks. Using predesigned hairpin structures as triggers, the network generates functional strands, which stabilize one or the other of the constituents of the network, leading to feedback-driven reconfiguration and time-dependent equilibration of the networks. Using structurally designed hairpins, positive-feedback or negative-feedback mechanisms operated by the CDNs are demonstrated. With two predesigned hairpins, the coupled consecutive operations of negative/positive- or positive/positive- feedback cascades are accomplished. The time-dependent composition changes of the networks are well reproduced by chemical kinetics simulations that provide predictive behaviors of the network, under variable auxiliary conditions. Beyond mimicking natural network properties and functions by means of the synthetic nucleic-acid-based CDNs, the systems introduce versatile perspectives for the design of amplified sensors (sensing of miRNA-376a) and the development of logic gate circuits.

Ultrafast geometrical reorganization of a methane cation upon sudden ionization: an isotope effect on electronic non-equilibrium quantum dynamics.

The ultrafast structural, Jahn-Teller (JT) driven, electronic coherence mediated quantum dynamics in the CH4+ and CD4+ cations that follows sudden ionization using an XUV attopulse exhibits a strong isotope effect. The JT effect makes the methane cation unstable in the Td geometry of the neutral molecule. Upon the sudden ionization the cation is produced in a coherent superposition of three electronic states that are strongly coupled and neither is in equilibrium with the nuclei. In the ground state of the cation the few femtosecond structural rearrangement leads first to a geometrically less distorted D2d minimum followed by a geometrical reorganization to a shallow C2v minimum. The dynamics is computed for an ensemble of 8000 ions randomly oriented with respect to the polarization of the XUV pulse. The ratio, about 3, of the CD4+ to CH4+ autocorrelation functions, is in agreement with experimental measurements of high harmonic spectra. The high value of the ratio is attributed to the faster electronic coherence dynamics in CH4+.

Electronic Coherences Steer the Strong Isotope Effect in the Ultrafast Jahn-Teller Structural Rearrangement of Methane Cation upon Tunnel Ionization.

We report on fully quantum electronic-nuclear dynamics following sudden ionization from the neutral in the three lowest electronic states of the CH4+ and CD4+ cations. There is a strong Jahn-Teller effect in the Franck-Condon region, and we employ two nuclear degrees of freedom that span the internal coordinates involved in the Jahn-Teller coupling. The initial state results from tunneling ionization by a strong IR field which coherently pumps the three lowest states of the cation, D0, D1, and D2. The quantum dynamical simulations show that a strong isotope effect occurs when the ionization significantly accesses the D2 state of the cation in the Franck-Condon region. The computed isotope effect is larger than expected on the basis of the effective mass ratio. The strong effect is due to fast oscillations of the electronic coherences between the D2 and the D1 and D0 electronic states and their modulation by the nonadiabatic couplings before a significant onset of nuclear motion. The magnitude of the effect is similar to the one that we previously reported for a sudden photoionization process. A strong isotope effect has been observed in high harmonic spectroscopy studies of the very short time dynamics Jahn-Teller structural rearrangement of the methane cation upon sudden ionization.

The density matrix via few dominant observables: The quantum interference in the isotope effect for atto-pumped N2.

Atto- and sub-femto-photochemistry enables preparation of molecules in a coherent superposition of several electronic states. Recently [Ajay et al., Proc. Natl. Acad. Sci. U. S. A. 115, 5890-5895 (2018)], we examined an effect of the nuclear mass during the non-adiabatic transfer between strongly coupled Rydberg and valence electronic states in N2 excited by an ultrafast pulse. Here, we develop and analyze an algebraic description for the density matrix and its logarithm, the surprisal, in such a superposition of states with a focus on the essentially quantum effect of mass. This allows for the identification of a few observables that accurately characterize the density matrix of the system with several coupled electron-nuclear states. We compact the time evolution in terms of time-dependent coefficients of these observables. Using the few observables, we derive an analytical expression for the time-dependent surprisal. This provides a mass-dependent phase factor only in the observables off-diagonal in the electronic index. The isotope effect is shown to be explicitly driven by the shift in the equilibrium position of the valence state potential. It is analytically given as a time-dependent phase factor describing the interference in the overlap of the two wave packets on the coupled electronic states. This phase factorizes as a product of classical and quantal contributions.

Compacting the density matrix in quantum dynamics: Singular value decomposition of the surprisal and the dominant constraints for anharmonic systems.

We introduce a practical method for compacting the time evolution of the quantum state of a closed physical system. The density matrix is specified as a function of a few time-independent observables where their coefficients are time-dependent. The key mathematical step is the vectorization of the surprisal, the logarithm of the density matrix, at each time point of interest. The time span used depends on the required spectral resolution. The entire course of the system evolution is represented as a matrix where each column is the vectorized surprisal at the given time point. Using the singular value decomposition (SVD) of this matrix, we generate realistic approximations for the time-independent observables and their respective time-dependent coefficients. This allows for a simplification of the algebraic procedure for determining the dominant constraints (the time-independent observables) in the sense of the maximal entropy approach. A non-stationary coherent initial state of a Morse oscillator is used to introduce the approach. We derive the analytical exact expression for the surprisal as a function of time, and this offers a benchmark for comparison with the accurate but approximate SVD results. We discuss two examples of a Morse potential of different anharmonicities, H2 and I2 molecules. We further demonstrate the approach for a two-coupled electronic state problem, the well-studied non-radiative decay of pyrazine from its bright state. Five constraints are found to be enough to capture the ultrafast electronic population exchange and to recover the dynamics of the wave packet in both electronic states.

Ultrafast fs coherent excitonic dynamics in CdSe quantum dots assemblies addressed and probed by 2D electronic spectroscopy.

We show in a joint experimental and theoretical study that ultrafast femto-second (fs) electronic coherences can be characterized in semi-conducting colloidal quantum dot (QD) assemblies at room temperature. The dynamics of the electronic response of ensembles of CdSe QDs in the solution and of QD dimers in the solid state is probed by a sequence of 3 fs laser pulses as in two-dimensional (2D) electronic spectroscopy. The quantum dynamics is computed using an excitonic model Hamiltonian based on the effective mass approximation. The Hamiltonian includes the Coulomb, spin-orbit, and crystal field interactions that give rise to the fine structure splittings. In the dimers studied, the interdot distance is sufficiently small to allow for an efficient interdot coupling and delocalization of the excitons over the two QDs of the dimer. To account for the inherent few percent size dispersion of colloidal QDs, the optical response is modeled by averaging over an ensemble of 2000 dimers. The size dispersion is responsible for an inhomogeneous broadening that limits the lifetimes of the excitonic coherences that can be probed to about 150 fs-200 fs. Simulations and experimental measurements in the solid state and in the solution demonstrate that during that time scale, a very rich electronic coherent dynamics takes place that involves several types of intradot and interdot (in the case of dimers) coherences. These electronic coherences exhibit a wide range of beating periods and provide a versatile basis for a quantum information processing device on a fs time scale at room temperature.

Time-dependent view of an isotope effect in electron-nuclear nonequilibrium dynamics with applications to N2.

Isotopic fractionation in the photodissociation of N2 could explain the considerable variation in the 14N/15N ratio in different regions of our galaxy. We previously proposed that such an isotope effect is due to coupling of photoexcited bound valence and Rydberg electronic states in the frequency range where there is strong state mixing. We here identify features of the role of the mass in the dynamics through a time-dependent quantum-mechanical simulation. The photoexcitation of N2 is by an ultrashort pulse so that the process has a sharply defined origin in time and so that we can monitor the isolated molecule dynamics in time. An ultrafast pulse is necessarily broad in frequency and spans several excited electronic states. Each excited molecule is therefore not in a given electronic state but in a superposition state. A short time after excitation, there is a fairly sharp onset of a mass-dependent large population transfer when wave packets on two different electronic states in the same molecule overlap. This coherent overlap of the wave packets on different electronic states in the region of strong coupling allows an effective transfer of population that is very mass dependent. The extent of the transfer depends on the product of the populations on the two different electronic states and on their relative phase. It is as if two molecules collide but the process occurs within one molecule, a molecule that is simultaneously in both states. An analytical toy model recovers the (strong) mass and energy dependence.

Personalized disease signatures through information-theoretic compaction of big cancer data.

Every individual cancer develops and grows in its own specific way, giving rise to a recognized need for the development of personalized cancer diagnostics. This suggested that the identification of patient-specific oncogene markers would be an effective diagnostics approach. However, tumors that are classified as similar according to the expression levels of certain oncogenes can eventually demonstrate divergent responses to treatment. This implies that the information gained from the identification of tumor-specific biomarkers is still not sufficient. We present a method to quantitatively transform heterogeneous big cancer data to patient-specific transcription networks. These networks characterize the unbalanced molecular processes that deviate the tissue from the normal state. We study a number of datasets spanning five different cancer types, aiming to capture the extensive interpatient heterogeneity that exists within a specific cancer type as well as between cancers of different origins. We show that a relatively small number of altered molecular processes suffices to accurately characterize over 500 tumors, showing extreme compaction of the data. Every patient is characterized by a small specific subset of unbalanced processes. We validate the result by verifying that the processes identified characterize other cancer patients as well. We show that different patients may display similar oncogene expression levels, albeit carrying biologically distinct tumors that harbor different sets of unbalanced molecular processes. Thus, tumors may be inaccurately classified and addressed as similar. These findings highlight the need to expand the notion of tumor-specific oncogenic biomarkers to patient-specific, comprehensive transcriptional networks for improved patient-tailored diagnostics.

Surprisal of a quantum state: Dynamics, compact representation, and coherence effects.

Progress toward quantum technologies continues to provide essential new insights into the microscopic dynamics of systems in phase space. This highlights coherence effects whether these are due to ultrafast lasers whose energy width spans several states all the way to the output of quantum computing. Surprisal analysis has provided seminal insights into the probability distributions of quantum systems from elementary particle and also nuclear physics through molecular reaction dynamics to system biology. It is therefore necessary to extend surprisal analysis to the full quantum regime where it characterizes not only the probabilities of states but also their coherence. In principle, this can be done by the maximal entropy formalism, but in the full quantum regime, its application is far from trivial [S. Dagan and Y. Dothan, Phys. Rev. D 26, 248 (1982)] because an exponential function of non-commuting operators is not easily accommodated. Starting from an exact dynamical approach, we develop a description of the dynamics where the quantum mechanical surprisal, a linear combination of operators, plays a central role. We provide an explicit route to the Lagrange multipliers of the system and identify those operators that act as the dominant constraints.

Time resolved mechanism of the isotope selectivity in the ultrafast light induced dissociation in N2.

The time evolution of a vacuum ultraviolet excited N2 molecule is followed all the way from an ultrafast excitation to dissociation by a quantum mechanical simulation. The primary aim is to discern the role of the excitation by a pulse short compared to the vibrational period, to discern the different coupling mechanisms between different electronic states, nonadiabatic, spin orbit, and to analyze the origin of any isotopic effect. We compare the picture in the time and energy domains. The initial ultrafast excitation pumps the molecule to a coherent electronic wave packet to which several singlet bound electronic states contribute. The total nonstationary wave function is given as a coherent sum of nuclear wave packets on each electronic state times the stationary electronic wave function. When the wave packets on different electronic states overlap, they are coupled in a mass-dependent manner whether one uses an adiabatic or a diabatic electronic basis. A weak spin-orbit coupling acts as a bottleneck between the bound singlet part of phase space and the triplet manifold of states in which dissociation takes place. To describe the spin-orbit perturbation that is ongoing in time, an energy-resolved eigenstate representation appears to be more intuitive. In the eigenstate basis, the singlet-to-triplet population transfer is large only between those vibronic eigenstates that are quasiresonant in energy. The states in resonance are different for different excitation energy ranges. The resonances are mass dependent, which explains the control of the isotope effect through the profile of the pulse.

Temporal and spatially resolved imaging of the correlated nuclear-electronic dynamics and of the ionized photoelectron in a coherently electronically highly excited vibrating LiH molecule.

Few-cycle ultrashort IR pulses allow excitation of coherently coupled electronic states toward steering nuclear motions in molecules. We include in the Hamiltonian the excitation process using an IR pulse of a definite phase between its envelope and carrier wave and provide a quantum mechanical description of both multiphoton excitation and ionization. We report on the interplay between these two processes in shaping the ensuing coupled electronic-nuclear dynamics in both the neutral excited electronic states and the cationic states of the diatomic molecule LiH. The dynamics is described by solving numerically the time-dependent Schrodinger equation at nuclear grid points using the partitioning technique with a subspace of ten coupled bound states and a subspace of discretized continuous states for the photoionization continua. We show that the coherent dynamics in the neutral subspace is strongly affected by the amplitude exchanges with the ionization continua during the pulse, as well as by the onset of nuclear motion. The coupling to the cation and the resulting ionization do not preclude the control of the motion in the neutral through control of the carrier-envelope phase. Our methodology provides visualization in space and in time not only of the entangled vibronic wave packet in the neutral states but also of the wave packet of the outgoing photoelectron. Thereby, we can spatially and temporally follow the dynamics of the outgoing and bound electrons during the pulse and the nuclear motion in the bound subspace while moving through nonadiabatic coupling regions after the pulse.

Intercellular signaling through secreted proteins induces free-energy gradient-directed cell movement.

Controlling cell migration is important in tissue engineering and medicine. Cell motility depends on factors such as nutrient concentration gradients and soluble factor signaling. In particular, cell-cell signaling can depend on cell-cell separation distance and can influence cellular arrangements in bulk cultures. Here, we seek a physical-based approach, which identifies a potential governed by cell-cell signaling that induces a directed cell-cell motion. A single-cell barcode chip (SCBC) was used to experimentally interrogate secreted proteins in hundreds of isolated glioblastoma brain cancer cell pairs and to monitor their relative motions over time. We used these trajectories to identify a range of cell-cell separation distances where the signaling was most stable. We then used a thermodynamics-motivated analysis of secreted protein levels to characterize free-energy changes for different cell-cell distances. We show that glioblastoma cell-cell movement can be described as Brownian motion biased by cell-cell potential. To demonstrate that the free-energy potential as determined by the signaling is the driver of motion, we inhibited two proteins most involved in maintaining the free-energy gradient. Following inhibition, cell pairs showed an essentially random Brownian motion, similar to the case for untreated, isolated single cells.

Intercommunication of DNA-Based Constitutional Dynamic Networks.

Intercommunication between dynamic chemical networks plays a major role in cellular transformations. Inspired by nature, we introduce the intercommunication between two constitutional dynamic networks, CDNs, "S" and "T" composed, each, of four equilibrated supramolecular constituents AA', AB', BA', and BB', and of CC', CD', DC', and DD', respectively. Each of the constituents is conjugated to a Mg2+-ion-dependent DNAzyme unit that acts as a reporter element for the concentration of the respective constituent via the catalyzed cleavage of the fluorophore/quencher-functionalized substrate associated with the respective DNAzyme reporter. Also, constituents BB' (in CDN "S") and CC' (in CDN "T") include Mg2+-ion-dependent DNAzymes acting as activator units for generating triggering signals between the networks. Subjecting CDNs "S" and "T" to the catalytically cleavable hairpin trigger Hdd' or Haa', respectively, yields input strands that intercommunicate the CDNs by affecting the time-dependent re-equilibration of the constituents of the counter CDN without affecting the dynamic equilibrium of the constituents of the CDN that generates the triggering strands. Treatment of CDNs "S" and "T" with hairpins Hdd' and Haa' (or Hba'), respectively, stimulates autonomous positive/positive or positive/negative feedback to the programmed time-dependent up-regulation or down-regulation of the equilibrated constituents in the two CDNs.