Related papers: On the correspondence between thermodynamics and i…
Chemical theories involving thermodynamical equilibrium states invariably utilize statistical mechanical equilibrium density distributions. Here, a definition of heat-work transformation termed thermo mechanical coherence is first made, and…
Our previous works have shown the statistical mechanics of self-gravitating system. In this paper, we will show its thermodynamics and compare our results with observations and simulations. We propose that our statistical mechanics can be…
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…
The traditional statistical inference is static, in the sense that the estimate of the quantity of interest does not affect the future evolution of the quantity. In some sequential estimation problems however, the future values of the…
In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states…
The Clausius inequality (CI) form of the second law of thermodynamics relates information changes (entropy) to changes in the first moment of the energy (heat and indirectly also work). Are there similar relations between other moments of…
We study the informational underpinnings of thermodynamics and statistical mechanics, using an abstract framework, general probabilistic theories, capable of describing arbitrary physical theories. This allows one to abstract the…
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…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…
Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct…
In a recent paper, Dunkel and Hilbert [Nature Physics 10, 67-72 (2014)] use an entropy definition due to Gibbs to provide a 'consistent thermostatistics' which forbids negative absolute temperatures. Here we argue that the Gibbs entropy…
We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic…
We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the…
Information based thermodynamic logic is revisited. It consists of two parts: Part A applies the modern theory of probability in which an arbitrary convex function \phi is employed as an analytic "device" to express information as…
We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with $\beta$-divergences. The resulting inference procedure is doubly robust for both the parameter and the…
Inference and learning are commonly cast in terms of optimisation, yet the fundamental constraints governing uncertainty reduction remain unclear. This work presents a first-principles framework inherent to Bayesian updating, termed…
We generalize the convex duality symmetry in Gibbs' statistical ensemble formulation, between Massieu's free entropy $\Phi_{V,N} (\beta)$ and the Gibbs entropy $\varphi_{V,N}(u)$ as a function of mean internal energy $u$. The duality tells…
The entropy production rate is a key quantity in non-equilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress towards its full grasping. By…