Related papers: On the correspondence between thermodynamics and i…
The long standing contrast between Boltzmann's and Gibbs' approach to statistical thermodynamics has been recently rekindled by Dunkel and Hilbert [1], who criticize the notion of negative absolute temperature (NAT), as a misleading…
We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the…
Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most…
This paper offers a pedestrian guide from the fundamental properties of entropy to the axioms of thermodynamics, which are a consequence of the axiom of statistical physics. It also dismantles flawed concepts, such as assigning physical…
Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicate details of the microscopic dynamics within a macroscopic system. The strength of Thermodynamics lies in…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi(a) \propto…
The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…
Machine learning algorithms often take inspiration from established results and knowledge from statistical physics. A prototypical example is the Boltzmann machine algorithm for supervised learning, which utilizes knowledge of classical…
This study proposes the novel Bayesian and inverse Bayesian (BIB) inference framework that incorporates symmetry bias into the Bayesian updating process to perform both conventional and inverse Bayesian updates concurrently. Conventional…
The act of measuring a system has profound consequences of dynamical and thermodynamic nature. In particular, the degree of irreversibility ensuing from a non-equilibrium process is strongly affected by measurements aimed at acquiring…
A generalization of the thermodynamic uncertainty relations is proposed. It is done by introducing of an additional term proportional to the interior energy into the standard thermodynamic uncertainty relation that leads to existence of the…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
The likelihood function plays a crucial role in statistical inference and experimental design. However, it is computationally intractable for several important classes of statistical models, including energy-based models and simulator-based…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…