Quantitative applicability of Rovelli's thermodynamic bound on agency-generated information to concrete physical agents

Rovelli's minimal thermodynamic model of agency (arXiv:2007.05300, 2020) describes an agent as a system A at temperature $T_a$, with heat capacity $C$ and long thermalization time $\tau_a$, interacting weakly and occasionally (cadence $\mathcal{T}$) with a colder world W at $T_w<T_a$ composed of N weakly coupled subsystems. Each interaction dissipatively selects one of N macroscopic alternatives, generating $I=\log_2 N$ bits of information at an entropy cost $\Delta S\sim C(\mathcal{T}/\tau_a)(\Delta T/T_w)$, so that $N<2^{(\mathcal{T}/\tau_a)(C\Delta T/T_w)}$, with a minimal binary choice requiring $C\Delta T\gg kT_w$. The model is deliberately minimal and has never been quantitatively connected to real agents: no mapping of concrete physical agents (biological organisms, brains, engineered devices) onto the model's parameters exists, no empirical estimates of those parameters, and no validation of the bound against real systems. The problem is to build this quantitative bridge — instantiate the model for concrete agents, estimate its parameters empirically, and determine whether the bound, or a needed refinement of the minimal model, actually governs agency-driven information generation in nature. The quantitative core has remained untouched in the literature, including Rovelli's own 2024 follow-up.

Background

In the physics of macroscopic irreversibility, an agent is any subsystem whose detailed dynamics we choose to disregard in a coarse-grained description, so that its 'choices' appear as unpredictable branchings of the macroscopic evolution. Rovelli's 'Agency in Physics' (2020) asks what makes such branching possible, why it is oriented toward the future, and where the information generated by a choice comes from, answering all three thermodynamically. The time orientation is traced to the second law together with the past hypothesis — the assumption that the entropy of the early universe was very low, which underlies the macroscopic arrow of time and is taken as a given input, not explained. The generation of information is traced to entropy growth, in the neighborhood of Landauer's principle (the established result that erasing one bit of information dissipates at least $kT\ln 2$ of energy at temperature $T$, where $k$ is Boltzmann's constant). The paper's core is a minimal model adapted from Rovelli's companion work 'Memory and Entropy' (2022): an agent A, a system at temperature $T_a$ with heat capacity $C$ (the proportionality between its thermal energy and temperature) and a long thermalization time $\tau_a$ (the timescale over which it equilibrates with its surroundings), interacts only occasionally — on average once every $\mathcal{T}$ seconds — and weakly ($\tau_a\gg\mathcal{T}$) with a world W at a lower temperature $T_w<T_a$ that is itself composed of $N$ subsystems which re-equilibrate quickly among themselves ($\tau_w\ll\mathcal{T}$). At each interaction, heat $Q=C T_a\mathcal{T}/\tau_a$ flows from the hotter agent to one randomly met subsystem of the colder world, raising that subsystem's macroscopic energy above the others: the interaction has thereby irreversibly selected one among $N$ macroscopic alternatives, producing $I=\log_2 N$ bits of Shannon information (the logarithm of the number of equiprobable alternatives) at an entropy cost

$$\Delta S\sim\frac{Q}{T_w}-\frac{Q}{T_a}\sim C\frac{\mathcal{T}}{\tau_a}\frac{\Delta T}{T_w},\qquad \Delta T=T_a-T_w.$$

Since information 'must come from somewhere', the necessary condition $I<\Delta S$ yields the bound

$$N<2^{(\mathcal{T}/\tau_a)(C\Delta T/T_w)},$$

and in the minimal case of a binary choice ($N=2$, $\mathcal{T}\ll\tau_a$) the excess thermal energy of the agent must exceed the per-degree-of-freedom thermal energy of the world: $C\Delta T\gg kT_w$. A non-vanishing temperature difference is thus a structural requirement for choice. Rovelli argues that quantum mechanics does not alter this thermodynamic account (quantum indeterminism reaches the macro-world only through decoherence, which is itself based on disregarding degrees of freedom), but develops no detailed quantum-statistical treatment; and he conjectures, speculatively, that this agency/memory mechanism converting low entropy into macroscopic information may be the principal source of the information exploited by biology and culture. The model is explicitly presented as minimal and illustrative: nowhere are the parameters $C$, $T_a$, $T_w$, $\tau_a$, $\tau_w$, $\mathcal{T}$ estimated for any real agent, nor is the bound confronted with data from organisms, brains, or engineered devices.

Problem Statement

Establish the quantitative applicability of the minimal thermodynamic model of agency (Rovelli 2020) to concrete physical agents — biological organisms, brains, and engineered devices. Specifically: (i) construct an explicit mapping of such an agent and its environment onto the model's variables — the agent's effective temperature $T_a$ and heat capacity $C$, the world's temperature $T_w$, the thermalization times $\tau_a$ and $\tau_w$, the interaction cadence $\mathcal{T}$, and the identifiable discrete choice events with their numbers of alternatives $N$; (ii) estimate these parameters empirically for concrete real systems, with stated data sources and uncertainties; (iii) test whether the information generated in the agents' actual choices is bounded by the associated entropy production as the model requires — through the bound $N<2^{(\mathcal{T}/\tau_a)(C\Delta T/T_w)}$ and the structural requirements $\Delta T>0$, $\tau_a\gg\mathcal{T}$, and the minimal binary condition $C\Delta T\gg kT_w$ (where $\Delta T=T_a-T_w$ and $k$ is Boltzmann's constant) — and establish that the test is non-vacuous, i.e. that it discriminates the minimal agency mechanism from generic second-law/Landauer bookkeeping rather than being satisfied by default; and (iv) where the minimal model fails to describe real agents, determine what refinement of it (e.g. coupling to non-thermal resources such as chemical potentials or light, multiple interaction channels) is required. Deliverables (i)-(iii) are required; deliverable (iv) is required only where the minimal model fails to describe the agents examined; and the empirical estimation (ii) must cover at least one well-characterised system in each of the three agent classes. The past hypothesis remains an input, as in the source. The common objective of all deliverables is a single quantitative answer: whether the entropy-to-information mechanism of the minimal model actually governs agency-driven information generation in real physical agents, at what scales, and with what accuracy.

References

1. Carlo Rovelli, 'Agency in Physics', arXiv:2007.05300 (2020), DOI 10.48550/arXiv.2007.05300, https://arxiv.org/abs/2007.05300
2. Carlo Rovelli, 'Memory and Entropy', Entropy 24(8):1022 (2022), DOI 10.3390/e24081022, https://doi.org/10.3390/e24081022 (arXiv:2003.06687)
3. Carlo Rovelli, 'The Thermodynamic Cost of Choosing', Foundations of Physics 54(3):28 (2024), DOI 10.1007/s10701-024-00765-7, https://doi.org/10.1007/s10701-024-00765-7 (arXiv:2309.08557)
4. Ali Barzegar, Emilia Margoni, Daniele Oriti, 'A minimalist account of agency in physics', Studies in History and Philosophy of Science 112:112-122 (2025), DOI 10.1016/j.shpsa.2025.06.004, https://doi.org/10.1016/j.shpsa.2025.06.004 (arXiv:2307.16054)
5. Rolf Landauer, 'Irreversibility and Heat Generation in the Computing Process', IBM Journal of Research and Development 5(3):183-191 (1961), DOI 10.1147/rd.53.0183, https://doi.org/10.1147/rd.53.0183
6. Antoine Bérut, Artak Arakelyan, Artyom Petrosyan, Sergio Ciliberto, Raoul Dillenschneider, Eric Lutz, 'Experimental verification of Landauer's principle linking information and thermodynamics', Nature 483:187-189 (2012), DOI 10.1038/nature10872, https://doi.org/10.1038/nature10872
7. Artemy Kolchinsky, David H. Wolpert, 'Semantic information, autonomous agency and non-equilibrium statistical physics', Interface Focus 8(6):20180041 (2018), DOI 10.1098/rsfs.2018.0041, https://doi.org/10.1098/rsfs.2018.0041 (arXiv:1806.08053)
8. Kate Jeffery, Robert Pollack, Carlo Rovelli, 'On the Statistical Mechanics of Life: Schrödinger Revisited', Entropy 21(12):1211 (2019), DOI 10.3390/e21121211, https://doi.org/10.3390/e21121211 (arXiv:1908.08374)
9. Emanuel Schwarzhans, Felix C. Binder, Marcus Huber, Maximilian P. E. Lock, 'Quantum measurements and equilibration: the emergence of objective outcomes via entropy maximisation', Physical Review Research 7:043279 (2025), DOI 10.1103/h2yj-25rn, https://doi.org/10.1103/h2yj-25rn (arXiv:2302.11253)
10. Aram Ebtekar, Marcus Hutter, 'Modeling the Arrows of Time with Causal Multibaker Maps', Entropy 26(9):776 (2024), DOI 10.3390/e26090776, https://doi.org/10.3390/e26090776
11. Huw Price, Ken Wharton, 'Bell Correlations as Selection Artefacts', arXiv:2309.10969 (2023), https://arxiv.org/abs/2309.10969
12. Laurens Walleghem, 'Are free choices absolute, when internalized in Wigner's friend?', arXiv:2605.14538 (2026), https://arxiv.org/abs/2605.14538
13. Nicolò Cangiotti, 'Becoming, Duration, and the Evolving Block Universe', arXiv:2607.03415 (2026), https://arxiv.org/abs/2607.03415
14. Guido Fioretti, 'A Physical and Mathematical Framework for the Semantic Theory of Evolution', arXiv:2503.18984 (2025), https://arxiv.org/abs/2503.18984
15. Bekir Baytaş, Ozan Ekin Derin, 'Category-theoretic formulation of relational materialism', arXiv:2409.02487 (2024), https://arxiv.org/abs/2409.02487
16. Ian Durham, 'A Formal Model for Adaptive Free Choice in Complex Systems', Entropy 22(5):568 (2020), DOI 10.3390/e22050568, https://doi.org/10.3390/e22050568