Boltzmann’s brain

Ludwig Boltzmann developed a statistical explanation of the second law of thermodynamics by defining entropy as being proportional to the logarithm of the number ways in which we can arrange a system [see ‘Entropy on the brain‘ on November 29th 2017].  The mathematical expression of this definition is engraved on his head-stone.  The second law states that the entropy of the universe is always increasing and Boltzmann argued it implies that the universe must have been created in a very low entropy state.  Four decades earlier, in 1854, William Thomson concluded the dissipation of heat arising from the second law would lead to the ‘death’ of the universe [see ‘Cosmic heat death‘ on February 18th, 2015] while the big bang theory for the creation of the universe evolved about twenty years after Boltzmann’s death.  The probability of a very low entropy state required to bring the universe into existance is very small because it implies random fluctuations in energy and matter leading to a highly ordered state.  One analogy would be the probability of dead leaves floating on the surface of a pond arranging themselves to spell your name.  It is easy to think of fluctuations that are more likely to occur, involving smaller systems, such as one that would bring only our solar system into existence, or progressively more likely, only our planet, only the room in which you are sitting reading this blog, or only your brain.  The last would imply that everything is in your imagination and ultimately that is why Boltzmann’s argument is not widely accepted although we do not have a good explanation for the apparent low entropy state at the start of the universe.  Jean-Paul Sartre wrote in his book Nausea ‘I exist because I think…and I cannot stop myself from thinking.  At this very moment – it’s frightful – if I exist, it is because I am horrified at existing.’  Perhaps most people would find horrifying the logical extension of Boltzmann’s arguments about the start of the universe to everything only existing in our mind.  Boltzmann’s work on statistical mechanics and the second law of thermodynamics is widely accepted and support the case for him being genius; however, his work raised more questions than answers and was widely criticised during his lifetime which led to him taking his own life in 1906.


Paul Sen, Einstein’s fridge: the science of fire, ice and the universe.  London: Harper Collins, 2021.

Jean-Paul Sartre, Nausea.  London: Penguin Modern Classics, 2000.

1 thought on “Boltzmann’s brain

  1. drehack

    While entropy, overall, will increase as stated clearly here, locally it can be reduced when free energy is available. Random fluctuations need to be countered by (re)ordering things. Life is a struggle to keep order – not only on your desk, but also in your body. However, order alone such as in a perfect crystal is meaningless. So, information and information processing is at the core of keeping a meaningful order.


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