Related papers: Partition function approach to non-Gaussian likeli…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we…
A pedagogical approach for deriving the statistical mechanical partition function, in a manner that emphasizes the key role of entropy in connecting the microscopic states to thermodynamics, is introduced. The connections between the…
I give a quick overview of some of the theoretical background necessary for using modern non-equilibrium statistical physics to investigate the thermodynamics of computation. I first present some of the necessary concepts from information…
The issue of discrete probability estimation for samples of small size is addressed in this study. The maximum likelihood method often suffers over-fitting when insufficient data is available. Although the Bayesian approach can avoid…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
Thermodynamics and information have intricate inter-relations. The justification of the fact that information is physical, is done by inter-linking information and thermodynamics - through Landauer's principle. This modern approach towards…
We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…
When partitioning workflows in realistic scenarios, the knowledge of the processing units is often vague or unknown. A naive approach to addressing this issue is to perform many controlled experiments for different workloads, each…
Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
We show that many theorems which assert that two kinds of partitions of the same integer $n$ are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics $X$ and…
We present a systematic study of the nested sampling algorithm based on the example of the Potts model. This model, which exhibits a first order phase transition for $q>4$, exemplifies a generic numerical challenge in statistical physics:…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical…
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean subset logic is usually mis-specified as the special case of…
I argue here that both the first and second laws of thermodynamics, generally understood to be quintessentially physical in nature, can be equally well described as being about certain types of information without the need to invoke…
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.…