This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known, ...the system then obeys an equation, which in the bulk and in the suitable limit tends to the Kramers–Langevin equation of physical kinetics. I consider time-dependent system-bath coupling and show that this leads to an additional harmonic force acting on the system. When the coupling is switched on and switched off rapidly, the force has delta-function support at the initial and final time. I further show that the work and heat functionals as recently defined in stochastic thermodynamics at strong coupling contain additional terms depending on the time derivative of the system-bath coupling. I discuss these terms and show that while they can be very large if the system-bath coupling changes quickly, they only give a finite contribution to the work that enters in Jarzynski’s equality. I also discuss that these corrections to standard work and heat functionals provide an explanation for non-standard terms in the change of the von Neumann entropy of a quantum bath interacting with a quantum system found in an earlier contribution (Aurell and Eichhorn, 2015).
Protein structure can be predicted in silico given sufficiently good templates, as demonstrated in successive installments of the biannual Critical Assessment of protein Structure Prediction (CASP) ...competition 1. Since the number of known protein sequences currently increases much faster than the number of known protein structures, and is likely to continue to do so in the foreseeable future, reliable ab initio protein structure prediction, without recourse to templates, would be highly desirable. The DCA starts from the knowledge of the whole multiple sequence alignment and not only from fi(k) and fij(k,l). ...Eq 1 is not the most unbiased representation of our knowledge of the system.\n The Problem The success of DCAs, which typically try to infer models with hundreds of thousands of parameters from thousands to tens of thousands of examples, can be phrased as the maxim "it is useful to learn exponential models of Big Data."
Direct-coupling analysis is a group of methods to harvest information about coevolving residues in a protein family by learning a generative model in an exponential family from data. In protein ...families of realistic size, this learning can only be done approximately, and there is a trade-off between inference precision and computational speed. We here show that an earlier introduced l2-regularized pseudolikelihood maximization method called plmDCA can be modified as to be easily parallelizable, as well as inherently faster on a single processor, at negligible difference in accuracy. We test the new incarnation of the method on 143 protein family/structure-pairs from the Protein Families database (PFAM), one of the larger tests of this class of algorithms to date.
Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D ...structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.
Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control ...can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.
The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the ...Feynman-Vernon influence functional formalism. This quantum entropy production has the form of the expectation value of three functionals of the forward and backward paths describing the system history in the Feynman-Vernon theory. In the classical limit of Kramers-Langevin dynamics (Caldeira-Leggett model) these functionals combine to three terms, where the first is the entropy production functional of stochastic thermodynamics, the classical work done by the system on the environment in units of kBT, and the second and the third other functionals which have no analogue in stochastic thermodynamics.
Genome-wide epistasis analysis is a powerful tool to infer gene interactions, which can guide drug and vaccine development and lead to deeper understanding of microbial pathogenesis. We have ...considered all complete severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genomes deposited in the Global Initiative on Sharing All Influenza Data (GISAID) repository until four different cutoff dates, and used direct coupling analysis together with an assumption of quasi-linkage equilibrium to infer epistatic contributions to fitness from polymorphic loci. We find eight interactions, of which three are between pairs where one locus lies in gene ORF3a, both loci holding nonsynonymous mutations. We also find interactions between two loci in gene nsp13, both holding nonsynonymous mutations, and four interactions involving one locus holding a synonymous mutation. Altogether, we infer interactions between loci in viral genes ORF3a and nsp2, nsp12, and nsp6, between ORF8 and nsp4, and between loci in genes nsp2, nsp13, and nsp14. The paper opens the prospect to use prominent epistatically linked pairs as a starting point to search for combinatorial weaknesses of recombinant viral pathogens.
We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of ...the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the non-interacting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well known fluctuation dissipation relation. Finally, we present numerical results for the heat current.
The observed intercellular heterogeneity within a clonal cell population can be mapped as dynamical states clustered around an attractor point in gene expression space, owing to a balance between ...homeostatic forces and stochastic fluctuations. These dynamics have led to the cancer cell attractor conceptual model, with implications for both carcinogenesis and new therapeutic concepts. Immortalized and malignant EBV-carrying B-cell lines were used to explore this model and characterize the detailed structure of cell attractors. Any subpopulation selected from a population of cells repopulated the whole original basin of attraction within days to weeks. Cells at the basin edges were unstable and prone to apoptosis. Cells continuously changed states within their own attractor, thus driving the repopulation, as shown by fluorescent dye tracing. Perturbations of key regulatory genes induced a jump to a nearby attractor. Using the Fokker–Planck equation, this cell population behavior could be described as two virtual, opposing influences on the cells: one attracting toward the center and the other promoting diffusion in state space (noise). Transcriptome analysis suggests that these forces result from high-dimensional dynamics of the gene regulatory network. We propose that they can be generalized to all cancer cell populations and represent intrinsic behaviors of tumors, offering a previously unidentified characteristic for studying cancer.
Symmetries of quantum evolutions Chiribella, Giulio; Aurell, Erik; Życzkowski, Karol
Physical review research,
07/2021, Letnik:
3, Številka:
3
Journal Article
Recenzirano
Odprti dostop
A cornerstone of quantum mechanics is the characterization of symmetries provided by Wigner's theorem. Wigner's theorem establishes that every symmetry of the quantum state space must be either a ...unitary transformation or an antiunitary transformation. Here we extend Wigner's theorem from quantum states to quantum evolutions, including both the deterministic evolution associated with the dynamics of closed systems and the stochastic evolutions associated with the outcomes of quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time-reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time-symmetric formulation of quantum theory must either restrict the set of the allowed evolutions or modify the operational interpretation of quantum states and processes. Here we propose a time-symmetric formulation of quantum theory where the allowed quantum evolutions are restricted to a suitable set, which includes both unitary evolution and projective measurements but excludes the deterministic preparation of pure states. The standard operational formulation of quantum theory can be retrieved from this time-symmetric version by introducing an operation of conditioning on the outcomes of past experiments.
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