Tightening the uncertainty principle for stochastic currents

We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic dissipation; and the analysis of thermodynamic consistency of the currents in the light of symmetries. Employing the large deviation techniques presented in [Gingrich et al., Phys. Rev. Lett. 2016] and [Pietzonka et al., Phys. Rev. E 2016], we provide a short proof of the loose uncertainty principle, and prove a tighter uncertainty relation for a class of thermodynamically consistent currents $J$. Our bound involves a measure of partial entropy production, that we interpret as the least amount of entropy that a system sustaining current $J$ can possibly produce, at a given steady state. We provide a complete mathematical discussion of quadratic bounds which allows to determine which are optimal, and finally we argue that the relationship for the Fano factor of the entropy production rate $\mathrm{var}\, \sigma / \mathrm{mean}\, \sigma \geq 2$ is the most significant realization of the loose bound. We base our analysis both on the formalism of diffusions, and of Markov jump processes in the light of Schnakenberg's cycle analysis.Comment: 13 pages, 4 figure

Effect of ultrasonic post-treatment on anaerobic digestion of lignocellulosic waste

This paper evaluates the effects of ultrasonication (US) applied, individually or in combination with a mechanical treatment, to the effluent of anaerobic digestion (AD) of lignocellulosic waste, on methane (CH4) production. US of the substrate downstream of AD is a relatively novel concept aimed at improving the degradation of recalcitrant components in order to enhance the overall energy efficiency of the process. US tests were carried out on real digestate samples at different energies (500−50,000 kJ/kg total solids (TS), corresponding to sonication densities of 0.08−0.45 W/ml). AD tests were performed on mixtures of sonicated (Sus) and untreated (S) substrate at two different Sus: S ratios (25:75 and 75:25 w/w), simulating post-sonicated material recycling to the biological process. The US effect was estimated through the solubilization degree of organic matter, as well as the CH4 production yield and kinetics, which were all found to be enhanced by the treatment. At Sus: S = 75:25 and Es ≥ 20,000 kJ/kg TS (0.25 W/ml), CH4 production improved by 20% and the values of the kinetic parameters increased by 64–82%

Generally covariant state-dependent diffusion

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously defined. They typically do not relax to equilibrium steady states even in the absence of extenal forces. Assuming both coordinate covariance and gauge invariance, we derive a second-order Langevin equation with state-dependent diffusion matrix and vanishing environmental forces. It differs from previous proposals but nevertheless entails the Einstein relation, a Maxwellian conditional steady state for the velocities, and the equipartition theorem. The over-damping limit leads to a stochastic differential equation in state space that cannot be interpreted as a pure differential (Ito, Stratonovich or else). At odds with the latter interpretations, the corresponding Fokker-Planck equation admits an equilibrium steady state; a detailed comparison with other theories of state-dependent diffusion is carried out. We propose this as a theory of diffusion in a heat bath with varying temperature. Besides equilibrium, a crucial experimental signature is the non-uniform steady spatial distribution.Comment: 24 page

Nonequilibrium thermodynamics as a gauge theory

We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.Comment: 6 pages. Non-fatal errors in eq.(6), eq.(26) and eq.(31) have been amende

Valorization of cheese-making residues in biorefineries using different combinations of dark fermentation, hydrothermal carbonization and anaerobic digestion

Dark fermentation (DF), hydrothermal carbonization (HTC) and anaerobic digestion (AD) are applied, in different combinations, to cheese whey (CW), which is the liquid effluent from the precipitation and removal of milk casein during the cheese-making process. The aim and novelty of this research is to investigate the production of various biofuels (H2-rich gas, hydrochar and biogas) in cascade, according to the waste biorefinery concept. The simplest case is the direct AD of CW. The second investigated possibility is the preliminary HTC of CW, producing hydrochar, followed by the AD of the process water from which hydrochar is separated by filtration. The third possibility is based on DF of CW, followed by the AD of the fermentate (F) from DF. The final possibility is based on DF of CW, followed by HTC of the F, and then AD of the process water. Accordingly, the physical and chemical properties of CW, F, resulting hydrochar and process water (PW), and biomethane potentials of CW, F, and process waters are studied to determine the energy and carbon balances of all variants. In brief, the first variant, direct AD of CW, is believed to be the most energy efficient method

Brownian Carnot engine

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Despite its potential relevance for the development of a thermodynamics of small systems, an experimental study of microscopic Carnot engines is still lacking. Here we report on an experimental realization of a Carnot engine with a single optically trapped Brownian particle as working substance. We present an exhaustive study of the energetics of the engine and analyze the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency -an insight that could inspire novel strategies in the design of efficient nano-motors.Comment: 7 pages, 7 figure

Full counting statistics of information content

We review connections between the cumulant generating function of full counting statistics of particle number and the R\'enyi entanglement entropy. We calculate these quantities based on the fermionic and bosonic path-integral defined on multiple Keldysh contours. We relate the R\'enyi entropy with the information generating function, from which the probability distribution function of self-information is obtained in the nonequilibrium steady state. By exploiting the distribution, we analyze the information content carried by a single bosonic particle through a narrow-band quantum communication channel. The ratio of the self-information content to the number of bosons fluctuates. For a small boson occupation number, the average and the fluctuation of the ratio are enhanced.Comment: 16 pages, 5 figure

Methods and conversations in (post)modern thermodynamics

Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues