The Fluctuation Theorem

«In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in thermostatted dissipative non-equilibrium systems. (…)

We take the assumption of causality to be axiomatic. It is causality which ultimately is responsible for breaking time reversal symmetry and which leads to the possibility of irreversible macroscopic behaviour. The Fluctuation Theorem does much more than merely prove that in large systems observed for long periods of time, the Second Law is overwhelmingly likely to be valid. The Fluctuation Theorem quantifies the probability of observing Second Law violations in small systems observed for a short time. (…)

The view that irreversibility is a result of our special place in space-time is still widely held [4]. In the present Review we will argue for an alternative, less anthropomorphic, point of view. (…)

One of the proofs of the Fluctuation Theorem given here, explicitly considers bundles of conjugate trajectory and antitrajectory pairs. (…)

In violation of the Second Law, heat energy from the surroundings can be converted into useful work to provide sufficient energy for the machine to run in reverse. This is an inescapable property of Nature which places a fundamental constraint on the operation of nanomachines. As you scale down machines they inescapably run in a mode: `two steps forward and one step back’. The ratio of forward to backward steps is given by the FT. This must also be the way that living sub-cellular organelles (machines) operate. (…)

It is logically possible that the Axiom of Causality could be replaced by its time conjugate: the Axiom of Anti-Causality. (…)

In an anticausal Universe, knowledge of its present state would enable us to predict the past but not the future.»

Denis J. Evans and Debra J. Searles, “The Fluctuation Theorem“, in Advances in Physics, 2002, Vol. 51, No. 7, 1529-1585.


«In other words, for a finite non-equilibrium system in a finite time, the Fluctuaction Theorem gives a precise mathematical expression for the probability that entropy will flow in a direction opposite to that dictated by the second law of thermodynamics.»


Só porque o verde me tolda a vista

Conhecia o poema de Pessoa sobre o verde, mas ainda não o havia experimentado.

Hoje compreendi-o perfeitamente, quando, à vinda do campo exterior numa tarde deveras ensolarada, entrei em casa e, em vez do normal efeito de encandeamento que se tem ao transitar para uma sala escura, vi tudo sob um verde intenso, como através de um filtro especial de uma máquina fotográfica.

E, portanto, como se não bastasse a acuidade acroamática, “cenas-fulgor”…

Torno-me criação contra vontade (ou, pelo menos, independentemente dela)…


Porque é que as cores têm força
De persistir na nossa alma,
Como fantasmas?
Há uma cor que me persegue, e hora a hora
A sua cor se torna a cor que é a minha alma. (…)

A náusea de todo o universo na garganta
Só por causa do verde,
Só porque o verde me tolda a vista,
E a própria luz é verde, um relâmpago parado de verde… (…)

Quanto pode um pedaço sobreposto
Pela luz à matéria escura… (…)

To Reality Winner

You don’t know me, neither do I know you, I mean, personally. What I do know is that Reality always wins. As a yoga practitioner, you also know that. Reality is the ultimate goal. All that is fake, sooner or later, falls, like a bad card, a cheating trump.

It is like life and death. People can kill wild weeds over and over. They can use toxics for a more persistent effect. They can even boost an entire Chernobyl site. But it won’t last. Weeds over time (say, centuries) will return and take the site again. Because they are more real, more alive, than the futile effort of disciplining or denaturing Nature.

Reality, you are young and the Force is with you (you had been in the Air Force, actually). And you are a clever woman who has learnt to decipher difficult foreign languages and also the language through which governments deceive populations.

I have read somewhere that, after being arrested, you tried to teach yoga to a woman who is a meth-addict. Ultimately, the whole country where you live is on a particular kind of hallucinogenic drug: manipulated news, unfair laws, fascist propaganda, persecution of brave and noble citizens (Aaron Swartz, Edward Snowden, and others).

As you noticed, we are oppressed by soulless orangutans, that excel in playing trumps or doing mimics for shows of “reality” (please note the inverted commas).

In fact, it is not only in US. It is happening all around the world. State policy is State police. The State is enemy of its own people. It doesn’t matter if it is the American State or the Islamic State or from somewhere else, their aim is always to produce statism and staticism, that is, preventing people from living according to the flow of Reality.

Your recently famous name is a sign that our desire for Reality is huge, that the virtue of Reality is ready for becoming actual.

And it will win, because it is closer to life than those livid exterminators (“white terrorists”) who control each one of our steps with barcode readers.

Be real!

The natural harmony willed by the melody

«Bird Song – Paul Dukas used to say, ‘Listen to the birds. They are great masters.’ I confess not to having awaited this advice to admire, analyse, and notate, some songs of birds. Through the mixture of their songs, birds make extremely refined jumbles of rhythmic pedals. Their melodic contours, those of merles especially, surpass the human imagination in fantasy. Since they use untempered intervals smaller then the semitone, and as it is ridiculous servilely to copy nature, we are going to give some examples of melodies of the ‘bird’ genre which will be transcription, transformation, and interpretation of the volleys and trills of our little servants of immaterial joy.» (p. 34)

«Paul Dukas often spoke of effects of resonance. Effects of pure fantasy, similar by a very distant analogy to the phenomenon of natural resonance. One will find remarkable ones, mingled with learned variations of rhythm, in the Danses rituelles and especially in the Mana of André Jolivet.» (p. 51)

«All these investigations ought not make us forget the natural harmony: the true, unique, voluptuously pretty by essence, willed by the melody, issued from it, pre-existent in it, having always been enclosed in it, awaiting manifestation. My secret desire of enchanted gorgeousness in harmony has pushed me toward those swords of fire, those sudden stars, those flows of blue-orange lavas, those planets of turquoise, those violet shades, those garnets of long-haired arborescence, those wheelings of sound and colors in a jumble of rainbows of which I have spoken with love in the Preface of my Quatuor pour la fin du Temps; such a gushing out of chords should necessarily be filtered; it is the sacred instinct of the natural and true harmony which, alone, can so charge itself». (p.52)

Olivier Messiaen, “Technique of My Musical Language”.

To make a point out of disappointment

«Peço que não faça como a gente vulgar, que é sempre reles (…)»

Fernando Pessoa, carta a Ophélia Queiroz, 29 Nov. 1920.


«Wo ist noch ein M[ensch] den man verehren* könnte! Aber ich kenne Euch Alle durch und durch.»

[Where there is still a human being that one can honour? But I know you all through and through!]

– Friedrich Nietzsche, fragment of a letter to Lou von Salomé and Paul Rée, Rapallo, around December 20, 1882.

* VEREHREN – German “ver” (prefix which denotes “increase”) + “Ehre” (honour).


«Death in life. There are people who are dead in life. And that’s the only death, that’s the real death. Not this death when you depart (…), but being dead when you’re alive, that’s real death, I think. (…) The most important thing about it is: he cannot adapt to this world and he should not adapt to it, since it is a bad world. There are two ways of looking at that: either you destroy this world – lock, stock and barrel – or you adjust to it in a way that you are detached from it. (…) I’ve always been interested in the occult, because I’ve never been able to accept this world. I know that there is another world behind it, that is the real world.»

Henry Miller, “The Henry Miller Odyssey” (1969).