A nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution

We discuss a nonlinear model for the relaxation by energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels e_i with i=1,2,...,N. The time-dependent occupation probabilities p_i(t) are assumed to obey the nonlinear rate equations tau dp_i/dt=-p_i ln p_i+ alpha(t)p_i-beta(t)e_ip_i where alpha(t) and beta(t) are functionals of the p_i(t)'s that maintain invariant the mean energy E=sum_i e_ip_i(t) and the normalization condition 1=sum_i p_i(t). The entropy S(t)=-k sum_i p_i(t) ln p_i(t) is a non-decreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions p_i(t) of the rate equations are unique and well-defined for arbitrary initial conditions p_i(0) and for all times. Existence and uniqueness both forward and backward in time allows the reconstruction of the primordial lowest entropy state. The time evolution is at all times along the local direction of steepest entropy ascent or, equivalently, of maximal entropy generation. These rate equations have the same mathematical structure and basic features of the nonlinear dynamical equation proposed in a series of papers ended with G.P.Beretta, Found.Phys., 17, 365 (1987) and recently rediscovered in S. Gheorghiu-Svirschevski, Phys.Rev.A, 63, 022105 and 054102 (2001). Numerical results illustrate the features of the dynamics and the differences with the rate equations recently considered for the same problem in M.Lemanska and Z.Jaeger, Physica D, 170, 72 (2002).Comment: 11 pages, 7 eps figures (psfrag use removed), uses subeqn, minor revisions, accepted for Physical Review

The smallest refrigerators can reach maximal efficiency

We investigate whether size imposes a fundamental constraint on the efficiency of small thermal machines. We analyse in detail a model of a small self-contained refrigerator consisting of three qubits. We show analytically that this system can reach the Carnot efficiency, thus demonstrating that there exists no complementarity between size and efficiency.Comment: 9 pages, 1 figure. v2: published versio

Axiomatic relation between thermodynamic and information-theoretic entropies

Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [Lieb, Yngvason, Proc. Roy. Soc.(2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalisation to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in non-equilibrium thermodynamics correspond to entropies used in one-shot information theory

A quantum solution to the arrow-of-time dilemma

The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.Comment: Contains slightly more material than the published version (the additional material is clearly labeled in the latex source). Because of PRL's title policy, the leading "A" was left out of the title in the published pape

Plasma Electronics

Contains reports on seventeen research projects.National Science Foundation (Grant GK-57)United States Atomic Energy Commission (Contract AT(30-1)-3285)United States Atomic Energy Commission under Contract AT(30-1)-322

Plasma Electronics

Contains reports on twelve research projects.United States Atomic Energy Commission (Contract AT(30-1)-3285)United States Atomic Energy Commission under Contract AT(30-1)-3221National Science Foundation (Grant GK-57

Plasma Dynamics

Contains reports on three research projects.United States Atomic Energy Commission (Contract AT(30-1)-1842)United States Air Force, Air Force Cambridge Research Center, Air Research and Development Command (Contract AF19(604)-5992)National Science Foundation (Grant G-9330)Flight Accessories Laboratory, Wright-Patterson Air Force Base (WADD Contract AF33(616)-3984

Plasma Electronics

Contains research objectives and reports on ten research projects.National Science Foundation (Grant GK-57)United States Atomic Energy Commission under Contract AT(30-1)-322

Impact of opioid-free analgesia on pain severity and patient satisfaction after discharge from surgery: multispecialty, prospective cohort study in 25 countries

Background: Balancing opioid stewardship and the need for adequate analgesia following discharge after surgery is challenging. This study aimed to compare the outcomes for patients discharged with opioid versus opioid-free analgesia after common surgical procedures.Methods: This international, multicentre, prospective cohort study collected data from patients undergoing common acute and elective general surgical, urological, gynaecological, and orthopaedic procedures. The primary outcomes were patient-reported time in severe pain measured on a numerical analogue scale from 0 to 100% and patient-reported satisfaction with pain relief during the first week following discharge. Data were collected by in-hospital chart review and patient telephone interview 1 week after discharge.Results: The study recruited 4273 patients from 144 centres in 25 countries; 1311 patients (30.7%) were prescribed opioid analgesia at discharge. Patients reported being in severe pain for 10 (i.q.r. 1-30)% of the first week after discharge and rated satisfaction with analgesia as 90 (i.q.r. 80-100) of 100. After adjustment for confounders, opioid analgesia on discharge was independently associated with increased pain severity (risk ratio 1.52, 95% c.i. 1.31 to 1.76; P < 0.001) and re-presentation to healthcare providers owing to side-effects of medication (OR 2.38, 95% c.i. 1.36 to 4.17; P = 0.004), but not with satisfaction with analgesia (beta coefficient 0.92, 95% c.i. -1.52 to 3.36; P = 0.468) compared with opioid-free analgesia. Although opioid prescribing varied greatly between high-income and low- and middle-income countries, patient-reported outcomes did not.Conclusion: Opioid analgesia prescription on surgical discharge is associated with a higher risk of re-presentation owing to side-effects of medication and increased patient-reported pain, but not with changes in patient-reported satisfaction. Opioid-free discharge analgesia should be adopted routinely