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A model to explain the statistics of the velocity gradients in the dissipation range of a turbulent flow is presented. The experimentally observed non-gaussian statistics is theoretically predicted by means of a thermodynamical analogy…
We give a broad generalisation of the mapping, originally due to Dennis, Kitaev, Landahl and Preskill, from quantum error correcting codes to statistical mechanical models. We show how the mapping can be extended to arbitrary stabiliser or…
The division by N! in the expression of statistical entropy is usually justified to students by the statement that classical particles should be counted as indistinguishable. Sometimes, quantum indistinguishability is invoked to explain it.…
Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory…
We study the information leakage to a guessing adversary in zero-error source coding. The source coding problem is defined by a confusion graph capturing the distinguishability between source symbols. The information leakage is measured by…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
The notion of entropy is shared between statistics and thermodynamics, and is fundamental to both disciplines. This makes statistical problems particularly suitable for reaction network implementations. In this paper we show how to perform…
We briefly introduce noise-based logic. After describing the main motivations we outline classical, instantaneous (squeezed and non-squeezed), continuum, spike and random-telegraph-signal based schemes with applications such as circuits…
Necessary conditions for asymptotically optimal sliding-block or stationary codes for source coding and rate-constrained simulation of memoryless sources are presented and used to motivate a design technique for trellis-encoded source…
In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium…
We develop a novel source coding strategy for sampling and monitoring of a Wiener process. For the encoding process, we employ a four level ``quantization'' scheme, which employs monotone function thresholds as opposed to fixed constant…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
This paper considers a sequential sensor scheduling and remote estimation problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process and makes a…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
We discuss several ways of illustrating fundamental concepts in statistical and thermal physics by considering various models and algorithms. We emphasize the importance of replacing students' incomplete mental images by models that are…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information transmission above which a given compact subset of the state…
We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential.…
We study a paradigm of coding for compression of the natural numbers via the zeta distribution and develop a statistical-mechanical interpretation, both in terms of Hagedorn systems and a Bose gas with energy levels given by logarithms of…
The rate coding response of a single peripheral sensory neuron in the asymptotic, near-equilibrium limit can be derived using information theory, asymptotic Bayesian statistics and a theory of complex systems. Almost no biological knowledge…