Related papers: A statistical mechanical interpretation of instant…
We study a stochastic version of the one-dimensional discrete nonlinear Schr{\"o}dinger equation (DNSE), which is derived from first principles, and thus possesses all the properties required by statistical mechanics, such as detailed…
The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…
We assess precision thermometry for an arbitrary single quantum system. For a $d$-dimensional harmonic system we show that the gap sets a single temperature that can be optimally estimated. Furthermore, we establish a simple linear…
We propose statistical systems based on $p$-adic numbers. In the systems, the Hamiltonian is a standard real number which is given by a map from the $p$-adic numbers. Therefore we can introduce the temperature as a real number and calculate…
This paper addresses fundamental aspects of statistical mechanics such as the motivation of a classical state space with spontaneous transitions, the meaning of non-equilibrium in the context of thermalization, and the justification of…
Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization $\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln…
We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size which is typical of critical phenomena. Our approach is to introduce an external,…
One of the major resource requirements of computers - ranging from biological cells to human brains to high-performance (engineered) computers - is the energy used to run them. Those costs of performing a computation have long been a focus…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of…
A computational theory for classification of natural biosonar targets is developed based on the properties of an example stimulus ensemble. An extensive set of echoes (84 800) from four different foliages was transcribed into a spike code…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite materials with complicated random microstructures remains a challenging issue. In this paper, we develop a novel statistical higher-order…
This article deals with the problem of the statistical performance analysis of the MUSIC ( Multiple Signal Classification ) algorithm which is an eigen decomposition based method for the estimation of the angles of arrival of signals…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
Depending on the exact experimental conditions, the thermodynamic properties of physical systems can be related to one or more thermostatistical ensembles. Here, we survey the notion of thermodynamic temperature in different statistical…
Cryptographic research takes software timing side channels seriously. Approaches to mitigate them include constant-time coding and techniques to enforce such practices. However, recent attacks like Meltdown [42], Spectre [37], and…
We evaluated the impact of changing the observation scale over the entropy measures for text descriptions. MIDI coded Music, computer code and two human natural languages were studied at the scale of characters, words, and at the…
Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface whose period is $\tau=\hbar/(k_{\rm B}T)$. Unfortunately, the standard theory is only…
A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the…