H-Theorems from Autonomous Equations

The H-theorem is an extension of the Second Law to a time-sequence of states that need not be equilibrium ones. In this paper we review and we rigorously establish the connection with macroscopic autonomy. If for a Hamiltonian dynamics for many particles, at all times the present macrostate determines the future macrostate, then its entropy is non-decreasing as a consequence of Liouville's theorem. That observation, made since long, is here rigorously analyzed with special care to reconcile the application of Liouville's theorem (for a finite number of particles) with the condition of autonomous macroscopic evolution (sharp only in the limit of infinite scale separation); and to evaluate the presumed necessity of a Markov property for the macroscopic evolution.Comment: 13 pages; v1 -> v2: Sec. 1-2 considerably rewritten, minor corrections in Sec. 3-

An extension of the Kac ring model

We introduce a unitary dynamics for quantum spins which is an extension of a model introduced by Mark Kac to clarify the phenomenon of relaxation to equilibrium. When the number of spins gets very large, the magnetization satisfies an autonomous equation as function of time with exponentially fast relaxation to the equilibrium magnetization as determined by the microcanonical ensemble. This is proven as a law of large numbers with respect to a class of initial data. The corresponding Gibbs-von Neumann entropy is also computed and its monotonicity in time discussed.Comment: 15 pages, v2 -> v3: minor typographic correctio

Derivation of quantum work equalities using quantum Feynman-Kac formula

On the basis of a quantum mechanical analogue of the famous Feynman-Kac formula and the Kolmogorov picture, we present a novel method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with previous methods in the literature, our method shows higher similarity in form to that deriving the classical fluctuation relations, which would give important insight when exploring new quantum fluctuation relations.Comment: 5 page

Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle

Second law of thermodynamics for macroscopic mechanics coupled to thermodynamic degrees of freedom

Based only on classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike recent identities between irreversible work and free energy, such as in the Jarzynski relation, the macroscopic dynamics is not governed by an external action but undergoes the back reaction of the microscopic degrees of freedom. Our theorems cover such physical situations as impact between macroscopic bodies, thermodynamic machines, and molecular motors.Comment: 4 pages, RevTe

Dynamical fluctuations for semi-Markov processes

We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov processes. Our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system, establishing some generic large deviation structures. We discuss in detail how the nonequilibrium driving and the non-exponential waiting time distribution influence the occupation-current statistics. The violation of the Markov condition is reflected in the emergence of a new type of nonlocality in the fluctuations. Explicit solutions are obtained for some examples of driven random walks on the ring.Comment: Minor changes, accepted for publication in Journal of Physics

Comparison of five different methods to assess the concentration of boar semen

Both for research and practical purposes, accurate and repeatable methods are required to assess the concentration of boar semen samples. Since the method which is used may influence the results considerably, the aim of the present study was to compare 5 frequently used techniques to determine boar semen concentration. Fifty ejaculates were collected from 37 different boars at an artificial insemination centre. Subsequently, each ejaculate was analyzed for sperm concentration by means of 2 different types of colorimeters (Colorimeter 1: Model 252, Sherwood Scientific Ltd, Cambridge, UK; Colorimeter 2: Ciba-Corning, Schippers, Bladel, The Netherlands), the Burker counting chamber (golden standard), and the Hamilton Thorne Analyzer (Ceros 42.1) using 2 types of Leja chambers (the 'former' and the 'recently developed'). Each ejaculate was assessed 5 times with each of the 5 methods, and the repeatability, expressed by coefficient of variation (CV), was determined for each method. The different methods were compared using Pearson's correlations and limits of agreement. The colorimeters yielded the lowest CV's (both 3.7%), while the former Leja chamber resulted in the highest CV (12.4%). Moreover, significant (P0.71) were found between the results obtained by the different methods. The limits of agreement plots showed that none of the methods consistently over- or underestimated the sperm concentrations when compared to the Burker chamber, although there was a tendency toward higher over- or underestimation in highly concentrated sperm samples. Based on our results, there were no major differences in the assessment of sperm concentration between the evaluated methods. The choice of method used in a laboratory could therefore be based on factors such as cost, number of samples to be assessed and practical use, without thereby negatively affecting the validity of the results thus obtained

Quantum Macrostates, Equivalence of Ensembles and an H-Theorem

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 observables. We propose an implementation of ideas that go back to John von Neumann's writing about the macroscopic measurement. We apply our scheme to the relation between macroscopic autonomy and an H-theorem, and to the problem of equivalence of ensembles. In particular, we show how the latter is related to the asymptotic equipartition theorem. The main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate, as the size of the system gets larger, on the macroscopic values for the different macroscopic observables. Deviations from that law are governed by the entropy.Comment: 16 pages; v1 -> v2: Sec. 3 slightly rewritten, 2 references adde