Related papers: A statistical mechanical interpretation of instant…
The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural…
Developing a thermodynamic theory of computation is a challenging task at the interface of non-equilibrium thermodynamics and computer science. In particular, this task requires dealing with difficulties such as stochastic halting times,…
The information spectrum approach gives general formulae for optimal rates of various information theoretic protocols, under minimal assumptions on the nature of the sources, channels and entanglement resources involved. This paper…
In statistical mechanics the zeroth law of thermodynamics is taken as a postulate which, as its name indicates, logically precedes the first and second laws. Treating it as a postulate has consequences for how temperature is introduced into…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…
The tradeoff relation between speed and cost is a central issue in designing fast and efficient information processing devices. We derive an achievable bound on thermodynamic cost for obtaining information through finite-time…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
An algorithmic limit of compressed sensing or related variable-selection problems is analytically evaluated when a design matrix is given by an overcomplete random matrix. The replica method from statistical mechanics is employed to derive…
In our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], we developed a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities at temperature T,…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. We identify the stochastic variable of the effective statistical theory that we derive as a…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short…
Despite extensive research, time series classification and forecasting on noisy data remain highly challenging. The main difficulties lie in finding suitable mathematical concepts to describe time series and effectively separate noise from…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
Noiseless coding theorem for finite stationary memoryless information sources is proved by using induction on the number of source symbols and the inequality of geometric and harmonic means.
The formalism used in describing the thermodynamics of abrupt (or first-order) phase transitions is reviewed as an application of maximum entropy inference. In this treatment, we show that the concepts of transition temperature, latent heat…
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…
Consensus is a common method for computing a function of the data distributed among the nodes of a network. Of particular interest is distributed average consensus, whereby the nodes iteratively compute the sample average of the data stored…