## Papers

• M. Polettini and M. Esposito,  Effective fluctuation and response theory, arXiv:1803.03552
[paper description]

• M. Polettini,  Oblique projections on metric spaces, arXiv:1711.04672

• M. Polettini and M. Esposito,  Effective thermodynamics for a marginal observer, Phys. Rev. Lett. 119, 240601 (2017), arXiv:1703.05715
[
paper description]

• G. Bisker, M. Polettini, T. R. Gingrich and J. M. Horowitz, Hierarchical bounds on entropy production inferred from partial information, J. Stat. Mech. 093210 (2017), arXiv:1708.06769

• M. Polettini and M. Esposito, Carnot efficiency at divergent power output,
Eur Phys. Lett. 118, 40003 (2017) , arXiv:1703.05715
[paper description]

• MP, A. Lazarescu, and M. Esposito, Tightening the uncertainty principle for stochastic currents, Phys. Rev. E 94, 052104 (2016), arXiv:1605.09692
[paper description]

• B. Altaner, MP, and M. Esposito, Fluctuation-Dissipation Relations Far from Equilibrium, Phys. Rev. Lett. 117, 180601 (2016), arXiv:1604.08832
[paper description]

• MP, G. Bulnes Cuetara and M. Esposito, Conservation laws and symmetries in stochastic thermodynamics, Phys. Rev. E 94, 052117 (2016), arXiv:1602.06555
[paper description]

• MP, A. Wachtel and M. Esposito, Dissipation in noisy chemical networks: The role of deficiency, J. Chem. Phys. 143, 184103 (2015), arXiv:1507.00058

• MP, BEST statistics of Markovian fluxes: a tale of Eulerian tours and Fermionic ghosts, J. Phys. A: Math. Theor. 48, 365005 (2015), arXiv:1503.03045
[paper description]

• MP, G. Verley and M. Esposito, Efficiency Statistics at All Times: Carnot Limit at Finite Power, Phys. Rev. Lett. 114, 050601 (2015), arXiv:1409.4716
[paper description]

• MP, Cycle/cocycle oblique projections on oriented graphs, Lett. Math. Phys. 105 , 89-107 (2015), arXiv:1405.0899
[paper description]

• MP and M. Esposito, Transient fluctuation theorem for the currents and initial equilibrium ensembles, J. Stat. Mech. P10033 (2014), arXiv:1408.5941

• MP, Fisher information of Markovian decay modes – Nonequilibrium equivalence principle, dynamical phase transitions and coarse graining, Eur. Phys. J. B 87 (9) , 215 (2014), arXiv:1409.4193

• MP and M. Esposito, Irreversible thermodynamics of open chemical networks I:
Emergent cycles and broken conservation laws
, J. Chem. Phys. 141, 024117 (2014), arXiv:1404.1181

• MP and M. Esposito, Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach, Phys. Rev. E. 88, 012112 (2013), arXiv:1304.6262

• MP, Fact-checking Ziegler’s maximum entropy production principle beyond the linear regime and towards steady states, Entropy 15, 2570-2584 (2013) [pdf], arXiv:1307.2052

• MP, Generally covariant state-dependent diffusion, J. Stat. Mech. P07005 (2013), arXiv:1206.2798

• MP, Diffusion in nonuniform temperature and its geometric analog, Phys. Rev. E 87, 032126 (2013), arXiv:1211.6580
[paper description]

• MP, Nonequilibrium thermodynamics as a gauge theory, Eur. Phys. Lett. 97, 30003 (2012), arXiv:1110.0608
[paper description]

• MP, Macroscopic constraints for the minimum entropy production principle, Phys. Rev. E 84, 051117 (2011), arXiv:1105.4131

## Conference proceedings, Ph.D. thesis, etc.

• MP, System/environment duality of nonequilibrium network observables,
Mathematical Technology of Networks Springer Proceedings in Mathematics & Statistics Volume 128, ed. Delio Mugnolo (Springer, 2015), pp 191-205, arXiv:1106.1280
[paper description]

• MP, Of dice and men. Subjective priors, gauge invariance, and nonequilibrium thermodynamics,
@ JETC2013, Brescia, Italy, July 1-5, 2013. [pdf]

• MP, Geometric and Combiatorial Structures in Nonequilibrium Statistical Mechanics,
Ph. D. thesis, Supervisor: Prof. Armando Bazzani (2012) [pdf]

## Other publications

• MP, Unspeakability of love,
Contribution to the interdisciplinary seminar “Being Singular Plural”, Guimaraes, December 2012 [pdf]

• MP, Paul Wilmott e l’abuso della matematica in finanza,
Il Sole 24 Ore, September 02, 2012 (in italian, newspaper title not mine) [pdf]

• MP, Paul Wilmott: lo ‘special QUANT’ e la crisi scientifica della finanza,
Il Corsaro, alternative news site (in italian) [pdf]

## Carnot efficiency at divergent power output

New paper out on the arXiv:

MP and M. Esposito, Carnot efficiency at divergent power output,
arXiv:1611.08192

It’s a very short and straightforward communication on a simple fact that nevertheless might have important consequences, and which was also noticed (one day in advance) in this preprint:

J. S. Lee and H. Park, Carnot efficiency is attainable in an irreversible process, arXiv:1611.07665

Engineering machines that have higher efficiency is a crucial technological problem. It is usually believed that optimal “Carnot” efficiency can only be realized via quasistatic processes that deliver zero power; this fact has been corroborated by several results, including a very recent inequality between power and efficiency by Shiraishi et al. [Phys. Rev. Lett. 117, 190601 (2016)]. However, this conclusion overlooks the important possibility that efficiency can be optimized in a dual scenario, that of divergent power. Starting from an observation that we briefly made in [Phys. Rev. Lett. 114, 050601 (2015)], where in an “extended linear regime” scenario we showed that there exists a limit where Carnot efficiency at divergent power output is possible, in this paper we go beyond the linear regime assumption, showing that, within the formalism of Stochastic Thermodynamics, Carnot efficiency can be achieved in the limit of a divergent power output in arbitrary stationary processes that have two coupled cycles.

## Efficiency Statistics at All Times: Carnot Limit at Finite Power

M. Polettini, G. Verley and M. Esposito,
Efficiency Statistics at All Times: Carnot Limit at Finite Power,
Phys. Rev. Lett. 114, 050601 (2015), arXiv:1409.4716

Enhancing the efficiency of energy conversion is the ultimate mission of thermodynamics. According to the paradigms of the phenomenological theory, it has long been believed that high efficiency can only be reached in processes that are infinitely slow and therefore useless for all practical purposes. However, there is no fundamental reason for this, and today we can investigate this question with the tools of a modern and powerful theory called Stochastic Thermodynamics. Stochastic Thermodynamics is capable of treating small systems that fluctuate; while fluctuations usually worsen the accuracy of processes, there exist critical conditions (e.g. near phase transitions) whereby small fluctuations are greatly enhanced, so to become structural properties. Following the proposal of Verley et al. [Verley 2014] to investigate efficiency in a probabilistic way, in this paper we investigate an analytically treatable model, that might be considered as the second-order approximation of any more complex model, where the thermodynamic currents are Gaussian and the efficiency statistics can be calculated exactly. The theory gives remarkable results, in particular there exists a nonvanishing probability that the system operates in reverse mode, i.e. that the power source is actually fed by the device it is supposed to power. This results in a bimodal probability distribution, a prediction of the theory that has already found partial experimental confirmation in an experiment on a small-scale Carnot engine [Martinez 2016]. Furthermore, at critical conditions our analysis shows that the Carnot efficiency can be maintained for long times at finite power output; hence we produced the first theoretical analysis of a system that has high efficiency but that needs not be infinitely slow. This observation has found further substantiation in a recent work relating critical scaling and efficiency enhancement [Campisi 2015]. Finally, other properties of the probability distribution of the efficiency can be shown to be universal, such as its power-law tails which imply that there is no average efficiency but only more probable efficiency. This explains the effect of the divergent average efficiency observed by certain authors in numerical simulations.

[Verley 2014] Verley, G., et al. “The unlikely Carnot efficiency. Nature communications, 5 (2014).

[Martinez 2016] Martínez, I. A., et al. “Brownian carnot engine.” Nature Physics 12.1 (2016): 67-70.

[Campisi 2015] Campisi, M. and Fazio, R. “Universality and scaling of optimal heat engines”, arXiv:1510.06183.

## Tightening the uncertainty principle for the currents

We have a new paper out in the arXiv! It’s a rather technical paper on how to improve on certain  thermodynamic uncertainty principles recently proved for stochastic dynamics.

The uncertainty principle of Heisenberg is one of the coolest concepts in all of physics, so it is not surprising that fields of research close and far to quantum mechanics have searched for similar principles, at times successfully. It has recently been the case for Stochastic Thermodynamics, the theory that formulates in a proper manner thermodynamics, extending it to nonequilibrium and fluctuating systems. The thermodynamic uncertainty principle roughly states that

“The more precise the measurement of a thermodynamic current, the greater the total mean dissipation”.

The more significant of our contributions to this subject is that we managed to replace the “total mean dissipation” by the “least possible mean dissipation in a system that can sustain that particular current” (given a whole bunch of other assumptions, of course…). A sort of minimum entropy production principle. Furthermore, we argued that uncertainty relation for the so-called Fano factor the dissipation rate $\sigma$

$\frac{\mathrm{var}\;\sigma}{\mathrm{mean}\;\sigma} \geq 2$

is the more significant of these uncertainty relations.

But that’s not what I want to talk about here. I’d rather collect a few random thoughts on quantum vs. stochastic uncertainties.

Uncertainty relations in quantum physics relate the variances of two canonically conjugate observables, such as position and momentum. The thermodynamic uncertainty displayed above relates the variance of the dissipation rate and its mean. This is indeed quite different: as usually the case, the temptation to reconnect quantum and stochastic phenomena hits against a square too much: probabilities are squared* wave functions, variances are squared* means etc. (*of course, not literally!).

However, in quantum physics a number of very different uncertainty relations have been derived. In particular I like the energy-time uncertainty relation. Strictly speaking, since time is not an operator but a parameter, there is no time-energy uncertainty in the same sense that there is position-momentum uncertainty. A quote attributed to Landau says that “To violate the time-energy uncertainty relation all I have to do is measure the energy very precisely and then look at my watch.” However, one can indeed make sense of such a relation in the following form:

“The uncertainty in time is expressed as the average time taken, starting in state ψ, for the expectation of some arbitrary operator A to change by its standard deviation.”

The quote is taken from the always excellent diary of John Baez. Now, that makes things much closer in spirit to the thermodynamic uncertainty principle, in that we are not talking about the variance of time, but of the actual time it takes to do something. And moreover, it confronts the variance and the expectation value of the same observable. This starts to echo to thermodynamic uncertainty principle. In particular, in this recent paper

E. Roldan et al., Decision making in the arrow of time, Phys. Rev. Lett. 115, 250602 (2015)

it is stated that

“The steady state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time”.

I find that things might actually converge somehow…