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Entropy production is a fundamental concept that plays a crucial role in the second law of thermodynamics and the measure of irreversibility. It imposes rigorous constraints on the kinds of transformations allowed in thermodynamic…
Active matter describes systems whose constituents convert energy from their surroundings into directed motion, such as bacteria or catalytic colloids. We establish a thermodynamic law for dilute suspensions of interacting active particles…
Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…
We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the…
A consequence of Ornstein theory is that the infinite entropy flows associated with Poisson processes and continuous-time irreducible Markov chains on a finite number of states are isomorphic as measure-preserving systems. We give an…
The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the mathematics of set partitions (which specify indefiniteness and definiteness) linearized to vector spaces, particularly in Hilbert spaces. That is,…
Continuous feedback control of Langevin processes may be non-Markovian due to a time lag between the measurement and the control action. We show that this requires to modify the basic relation between dissipation and time-reversal and to…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
We explore a previously unknown connection between two important problems in physics, i.e., quantum macroscopicity and the quantum phase transition. We devise a general and computable measure of quantum macroscopicity that can be applied to…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
We address the emergence of entropy production in the non-equilibrium process of an open quantum system from the viewpoint of the environment. By making use of a dilation-based approach akin to Stinespring theorem, we derive an expression…
Reciprocal relations correlate fairly accurately a great variety of experimental results. Nevertheless, the concepts of statistical fluctuations, and microscopic reversibility - the bases of the accepted proof of the relations by Onsager -…
The irreversibility in a statistical system is traced to its probabilistic evolution, and the molecular chaos assumption is not its unique consequence as is commonly believed. Under the assumption that the rate of change of the each…
Entropy production is the crucial quantity characterizing irreversible phenomena and the second law of thermodynamics. Yet, a ubiquitous definition eludes consensus. Given that entropy production arises from incomplete access to…
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to…
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…
Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
Sequences diverge either because they head off to infinity or because they oscillate. Part 1 constructs a non-Archimedean framework of infinite numbers that is large enough to contain asymptotic limit points for non-oscillating sequences…