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Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several…
In this paper, the base of quantum mechanics is the spontaneous tendency for a microscopic object to fractionalize instantly into quasistates and condense instantly quasistates. This quasistate is equivalent to the eigenfunction. An object…
We develop an information-theoretic reconstruction of quantum dynamics based on inference over action space. The fundamental object is a density of action states encoding the multiplicity of dynamical alternatives between configurations.…
In this paper, the suggested similarity between micro and macro-cosmos is extended to quantum behavior, postulating that quantum mechanics, like general relativity and classical electrodynamics, is invariant under discrete scale…
Two generalizations of It\^o formula to infinite-dimensional spaces are given. The first one, in Hilbert spaces, extends the classical one by taking advantage of cancellations, when they occur in examples and it is applied to the case of a…
Generic far-away-from-equilibrium many-body dynamics involve entropy production, and hence are thermodynamically irreversible. Near quantum critical points, an emergent conformal symmetry can impose strong constraints on entropy production…
We propose an additional category of dimensionless groups based on the principle of {\it entropic similarity}, defined by ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes.…
Motivated by the asymptotic collective behavior of random and deterministic matrices, we propose an approximation (called "free deterministic equivalent") to quite general random matrix models, by replacing the matrices with operators…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
In this article a definition of reversible processes in terms of differences in intensive Thermodynamics properties (Affinities) is proposed. This definition makes it possible to both define reversible processes before introducing the…
A pedagogical derivation of statistical mechanics from quantum mechanics is provided, by means of open quantum systems. Besides, a new definition of Boltzmann entropy for a quantum closed system is also given to count microstates in a way…
Based on the equivalence of the two different types of measurement protocols and the asymmetry between the Schr\"odinger and Heisenberg pictures, it has been previously proposed that negative sea fills the universe as a nondeterministic…
We make precise sense of the idea of "molecular chaos" through algorithmic randomness of microscopic trajectories, and ground macroscopic irreversibility in the lack of symmetry under time reversal of this property. This concept of…
We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution.…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
Microscopic quantum laws are time-symmetric: nothing in the Schr\"odinger equation or its relativistic extensions distinguishes future from past. Yet measurements produce irreversible records, an apparently one-way causal flow, and the…
In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics…
A legend tells that once Loschmidt asked Boltzmann on what happens to his statistical theory if one inverts the velocities of all particles, so that, due to the reversibility of Newton's equations, they return from the equilibrium to a…
Within the general formalism of quantum theory irreversibility and the arrow of time in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of entropy production. This motivates…
Stochastic thermodynamics gives universal relations for microscopic entropy production, yet its critical behavior at macroscopic nonequilibrium transitions remains unclassified. We study well-mixed reversible chemical reaction networks in…