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Time-energy uncertainty principle for irreversible heat engines.

ABSTRACT: Even though irreversibility is one of the major hallmarks of any real-life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck's constant at the length scale of the order Bohr radius, i.e. the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

SUBMITTER: Hanel R

PROVIDER: S-EPMC7134951 | biostudies-literature | 2020 May

REPOSITORIES: biostudies-literature

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Time-energy uncertainty principle for irreversible heat engines.

Hanel Rudolf R Jizba Petr P

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 20200330 2170

Even though irreversibility is one of the major hallmarks of any real-life process, an actual understanding of irreversible processes remains still mostly semi-empirical. In this paper, we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle is bounded from below by an irreducible and ...[more]

PMID: 32223412

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Project description:BackgroundThis study was designed to evaluate if erythropoietin (EPO) is effective in the treatment of cancer related anemia, and if its effect remains unchanged when data are analyzed according to various clinical and methodological characteristics of the studies. We also wanted to demonstrate that cumulative meta-analysis (CMA) can be used to resolve uncertainty regarding clinical questions.MethodsSystematic Review (SR) of the published literature on the role of EPO in cancer-related anemia. A cumulative meta-analysis (CMA) using a conservative approach was performed to determine the point in time when uncertainty about the effect of EPO on transfusion-related outcomes could be considered resolved.ParticipantsPatients included in randomized studies that compared EPO versus no therapy or placebo.Main outcome measuresNumber of patients requiring transfusions.ResultsNineteen trials were included. The pooled results indicated a significant effect of EPO in reducing the number of patients requiring transfusions [odds ratio (OR) = 0.41; 95%CI: 0.33 to 0.5; p < 0.00001;relative risk (RR) = 0.61; 95% CI: 0.54 to 0.68]. The results remain unchanged after the sensitivity analyses were performed according to the various clinical and methodological characteristics of the studies. The heterogeneity was less pronounced when OR was used instead of RR as the measure of the summary point estimate. Analysis according to OR was not heterogeneous, but the pooled RR was highly heterogeneous. A stepwise metaregression analysis did point to the possibility that treatment effect could have been exaggerated by inadequacy in allocation concealment and that larger treatment effects are seen at hb level > 11.5 g/dl. We identified 1995 as the point in time when a statistically significant effect of EPO was demonstrated and after which we considered that uncertainty about EPO efficacy was resolved.ConclusionEPO is effective in the treatment of anemia in cancer patients. This could have already been known in 1995 if a CMA had been performed at that time.

Project description:Despite the remarkable success of Carnot's heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr2ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr2ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck's quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine's inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot's calorique, or the non-sensible heat later described by Clausius as 'work-heat', exclusively to negative Gibbs energy (-G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth's climates.

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Time-energy uncertainty principle for irreversible heat engines.

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Time-energy uncertainty principle for irreversible heat engines.

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