Inspired by foundational studies in classical and quantum physics, and by information retrieval studies in quantum information theory, we prove that the notions of ‘energy’ and ‘entropy’ can be consistently introduced in human language and, more generally, in human culture. More explicitly, if energy is attributed to words according to their frequency of appearance in a text, then the ensuing energy levels are distributed non-classically, namely, they obey Bose–Einstein, rather than Maxwell–Boltzmann, statistics, as a consequence of the genuinely ‘quantum indistinguishability’ of the words that appear in the text. Secondly, the ‘quantum entanglement’ due to the way meaning is carried by a text reduces the (von Neumann) entropy of the words that appear in the text, a behaviour which cannot be explained within classical (thermodynamic or information) entropy. We claim here that this ‘quantum-type behaviour is valid in general in human language’, namely, any text is conceptually more concrete than the words composing it, which entails that the entropy of the overall text decreases. In addition, we provide examples taken from cognition, where quantization of energy appears in categorical perception, and from culture, where entities collaborate, thus ‘entangle’, to decrease overall entropy. We use these findings to propose the development of a new ‘non-classical thermodynamic theory’ for human cognition, which also covers broad parts of human culture and its artefacts and bridges concepts with quantum physics entities. This article is part of the theme issue ‘Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)’.