aa r X i v : . [ phy s i c s . h i s t - ph ] J u l Agency in Physics
Carlo Rovelli
Aix Marseille University, Universit´e de Toulon, CNRS, CPT, 13288 Marseille, France.Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, Canada, N2L 2Y5.The Rotman Institute of Philosophy, 1151 Richmond St. N London, Ontario, Canada, N6A 5B7. (Dated: July 14, 2020)I discuss three aspects of the notion of agency from the standpoint of physics: (i) what makes aphysical system an agent; (ii) the reason for agency’s time orientation; (iii) the source of the infor-mation generated in choosing an action. I observe that agency is the breaking of an approximationunder which dynamics appears closed. I distinguish different notions of agency, and observe thatthe answer to the questions above differ in different cases. I notice a structural similarity betweenagency and memory, that allows us to model agency, trace its time asymmetry to thermodynami-cal irreversibility, and identify the source of the information generated by agency in the growth ofentropy. Agency is therefore a physical mechanism that transforms low entropy into information.This may be the general mechanism at the source of the whole information on which biology builds.
I. THE PROBLEM
Agency is the possibility for an agent to act on theworld, and affect it. The notion of agency is used ina variety of contexts, with variable meanings. Agentsplay a role in areas spacing from economy to theology.They are increasingly utilised in foundational contexts,for instance in discussing the conceptual basis of thermo-dynamics [1, 2], quantum mechanics [3], causality [4–7],even the foundations of physics itself [8].Agency raises three questions for a physicist. First,how to understand the assumed independence of theagent and its possibility of alternative choices, given thatreal agents are themselves physical systems that do notviolate laws of nature. Second, agency affects the future,not the past: what is the origin of the time asymmetry,considering that the elementary laws of physics are in-variant under time reversal? Third, an agent can choosealternative courses of action and the choice generates in-formation: an agent can pick one among N alternatives,generating I = log N bits of information. Where doesthis information originate from?Here I consider a solutions to these three questions.On various other recent physical perspectives on agency,see [9–12] and references therein. A perspective similarto the one considered here has been independently de-veloped very recently by Barry Loewer in [13]. I give forunderstood that nothing in agency conflicts with knownlaws of nature; but understanding how the actual be-haviour that we denote agency can be accounted for interms of these laws is something that requires a bit ofthinking. This is what is done here.To this end, I consider a general characterisation ofagency, but also distinguish distinct manners in whichthe notion of agency is intended and used. These cap-ture different degrees of the independence, or freedom,we attribute to the agent.To account for agency’s time asymmetry we cannot re-cur to the time orientation of the agent’s perspective (asis done in many contexts), because this is what we wantto account for, not to assume. The only viable alterna- tive is to trace it to the manifest time-asymmetry of themacroscopic world. This, in turn, is accounted for by thesecond principle of thermodynamics, widely understood;by which I mean here the genericity assumption of statis-tical physics plus (the non-genericity assumption of) thepast hypothesis [14], namely the fact that entropy waslow in the past. The time orientation of agency must beultimately rooted in the second principle because there isnothing else at our disposal [15, 16]. As we shall see, how-ever, this is realised indirectly and in different ways fordifferent kinds of agencies. The core of the paper is Sec-tion IV, where I show how the dots between thermody-namics and agency can be filled-in, using a simple modelthat illustrates how entropy growth can drive agency.The model presented here derives from a structuralsimilarity between agency and memory, and a recent re-sults on the relation between memory and entropy [17].In particular, the model yields a thermodynamical boundon the information produced in agency, tying the gener-ation of information to thermodynamical parameters.Memory and agency can thus be viewed as mechanismsthat convert free energy into information. This may wellbe the primary source of the information the biosphere,the brain, and culture, deal with. II. THE AGENT AS A PHYSICAL SYSTEM
The key to address the nature of agency, is to recognisethat agency does not refer solely to events in the world:it refers to a manner of description of these events. Thenotion of agency is grounded in ignoring physical links,namely some of the physical (deterministic or probabilis-tic) correlations described by the physical laws.
A. Agency is disregarding physical links
To illustrate this idea, consider the use of agency inthe foundations of thermodynamics or quantum theory.A fertile formulation of both of these theories is to seethem describing the response of physical systems (ther-modynamical or quantum) when they are acted upon incertain manners. For instance: ‘If we compress the vol-ume of a gas, the temperature increases so and so’. Or:‘If we prepare a q-bit in this state, and then measure thisspin, we obtain this number’. These are descriptions ofbehaviours of a part of the world, when an agent actson it one way or the other. The language of agency isexplicit in numerous presentations of these theories, andis sometimes deemed essential.A moment of reflection, however, shows that this lan-guage can be translated away. Any occurrence of ‘if anagent acts on the system in this and that manner’ canbe translated into a statement of the form ‘if the systemhappens to interact in this and that manner’; thus trad-ing the independence of the agent with the modality thatis at the basis of all physical laws.Physical laws, indeed, refer to regularities, namely torepetitive behaviour happening under repeated circum-stances. They are generically of the form ‘Anytime thatA then also B’, or ‘anytime that A then the probability ofB is so and so’. The ‘anytime’ is a conditional (‘if’). Thephase space of classical mechanics and the Hilbert spaceof quantum theory are spaces of possibilities, where theconditionals reside. Laws have been found, in principle,by generalisation and induction out of a number of re-peated observations. Hence the notion of an agent ‘freeto act’ is actually irrelevant in the foundations of ther-modynamics and quantum theory: it can be replaced bythe conditional: ‘whenever this, then that’.But the opposite is equally true. And it is more inter-esting. Precisely because physics is modal in this manner,we can always replace the conditionals with the action ofan independent agent. And express the arbitrariness byattributing it to something that we call ‘agency’. There-fore the agent is here simply the place where we arbitrar-ily decide to start the sequence of correlations describedby the laws we are interested in: it is, in other words,where we ignore previous physical links.To illustrate this, consider for instance the statementthat the temperature of a mass of real gas increases whencompressed. The compression is due to the interactionbetween the gas and some other physical system. Thisother physical system can be a human agent freely decid-ing to push a piston; but also the wind pushing a massof atmospheric air downhill along a mountain. For thegas, which is what is being considered, the difference isirrelevant: the human and the wind are ‘agents’. Whatmakes them agents, here, is simply the fact that in de-scribing the behaviour of the gas we are not interested inthe chain of physical links they might happen to follow:these are treated as external, arbitrary. It is this thatmakes them agents here: ignoring their physics.This is in fact general. Agency is always associatedto the boundaries of an incomplete or approximate de-scription of the world, within which physical links are tosome extent closed, namely approximately sufficient toaccount for the evolution. It refers to the spots where the physical links are ignored. The agent is the systemwhose physical links are neglected in a given account.To see how this works in general, however, we have todistinguish variants of the notion of agency.
B. Different notions of agency
In a wide sense, any physical system acting on a secondsystem and affecting it can be called an agent. But theword ‘agency’ is commonly employed in a more restrictedsense, indicating the capacity of certain systems, such ashumans, to take independent, autonomous, intentionaldecisions and act on these.The ambiguity in the use of the term is reflected in thephilosophical debate about agency (see for instance [18]and references there). From the perspective of physics,the ambiguity refers to the assumptions about the rea-sons for an agent to act in one way or the other. There isa spectrum of (overlapping) possibilities, leading to dis-tinct notions of agency, which can be denoted as follows.We can call:
External agent: any system, when we simply disregardthe reasons for its behaviour. Example: in dealingwith the dynamics of the Moon’s surface, a me-teorite that impacts on its surface is an externalagent.
Internal agent: a system governed by some complex in-ternal dynamics which we could reconstruct. Ex-ample: This computer is the agent that controlsthat door.
Random agent: a system governed by a genuinely prob-abilistic dynamics.
Independent agent: a system governed by an internal(deterministic or probabilistic) dynamics, too com-plex for us to reconstruct. Example: This man isthe agent that decides whether to open that door.
Supernatural agent: a system that does not satisfy nei-ther deterministic nor probabilistic physical laws.
External agency is only a way of talking about externalphysical links when we are not interested in accountingfor them.
Random agency can be instantiated by quan-tum theory. Human agency is an example of independent agency [19, 20]. The existence of agency that does notto satisfy neither deterministic nor probabilistic physicallaws ( supernatural ) would contradict our current under-standing of our world I see no interest in considering it.The most interesting case is independent agency, in par-ticular when the agent can choose between alternativesthat affect the world differently. In Section IV we shallsee how a physical system can actually do so.
III. TIME ORIENTATION
Agency is time oriented: it affects the future, not thepast. What is the source of this time asymmetry? Theanswer is delicate, because it differs for different notionsof agency [15].
A. Perspectival time orientation
Let’s start with the simplest case. Consider an elasticcollision between a ball B and a ball B . When it is hitby B , the ball B changes its velocity. Say the velocitybefore the collision was ~v past and after the collision itbecomes ~v future . We can say that B has acted on B andthe effect of this action is in the future: it has changed ~v past into ~v future . This is a possible example of an actionaffecting the future.However, the physical laws governing the collision aretime reversible. There is nothing in the process itselfthat picks up a time direction. At given past ~v past , it isthe future to be affected by the act; but at given future ~v future , it is the past to be affected. That is: at fixedpast, the world with the collision and the world withoutthe collision have a different future; while at fixed future,the world with the collision and the world without thecollision have a different past. We could equally describethe same history backward in time, with the same laws,and say that the effect of the interaction has been tochange the velocity from ~v future to ~v past .The reason we say that the collision affects the trajec-tory of the particle B after the collision is only to befound in the regard we give to the phenomenon. It is we who are time oriented. In turn, the reason we take thepast as fixed is that we can remember it and we cannotinfluence it, while we cannot remember the future andwe can influence it. Hence we consider the past states ofthe two balls as given, and we say that the effect of thecollision is in the future. The distinction refers to what we know, not to anything in the phenomenon itself. Thedistinction is perspectival. As far the phenomenon aloneis concerned, it is purely linguistic: we simply call effectwhat happens after the collision [21].It is tempting to jump from this to saying that this isall there is to say about the time orientation of agency:it is perspectival, agency looks time oriented, but it isonly because we see it so. But that would be a mistake.The reason is that we have simply displaced the prob-lem: the collision does not distinguish cause froms effect,but we do. And our distinction is rooted in our ownagency, which can affect the future but not the past. Thephenomena determined by us and our agency —and withus a large class of other systems we call internal agents—are definitely not time symmetric.In particular, to have a different effect on the ball B ,a different motion of the ball B is needed, while I cannow choose between different macroscopic futures giventhe same macroscopic past. What is the source of timeorientation in this case? B. Physical time orientation
It is not difficult to find the source of time-orientedphenomena: the entire macroscopic world around us ismanifestly time oriented. We understand this time ori-entation of the macro-world in terms of the second prin-ciple (in a generalised sense, and including the past hy-pothesis) which is the only ‘fundamental’ law that breakstime-reversal invariance. There is no reason for agencyto be different, and there is no other source of time ori-entation available in our universe (see below for a discus-sion about quantum theory). Agency must therefore bea macroscopic phenomenon governed by an entropy gra-dient (and ultimately the past hypothesis of a primordiallow entropy that underpins it) [15, 16]. This must be theground for the orientation of complex agents like us.This is the only possible answer to the question of theorigin of the time orientation of agency, in the context ofa naturalistic perspective. The main question I addressin this paper is how an entropy gradient can give rise tothe behaviour we recognise as agency. As we shall seein the next Section, the additional ingredients needed forthis are surprisingly meagre.The subtle point is the fact that it is the macroscopic world to be time oriented. The micro-history of realityhappens to be such that in a direction of time (the ‘past’)the microstate belonged to a low entropy macrostate.(To even state time orientation we need to have a notionof macrostates, namely a coarse graining.) Accordingly,agency must be accounted form in terms of a macro-scopic/microscopic distinction, in the sense of statisticalmechanics and thermodynamics.This is not a distinction on the basis of size, scale, ornumber of degrees of freedom; it is a distinction relativeto a set variables (called macroscopic), to which we haveaccess and that have a partially closed dynamics withinsome approximation. That is, their behaviour can beapproximately determined without involving other vari-ables. (Here I take low initial entropy, or the past hy-pothesis, as given: I do not discuss the possibility foritself to be perspectival, which is discussed in [22].)Now, consider an internal agent. If we described itin complete mechanical terms, the time orientation ofagency would again be just a linguistic choice. But, aswe have seen in the previous Section, an agent is preciselya system of which we are disregarding part the dynamics.When we describe a human being as an agent, we are ob-viously not describing its complete microphysics. Hence,the separation between manifest (macroscopic) degrees offreedom and underlying (microscopic) ones that are notaccounted for is constitutive to the notion of independentagency [19]. It is precisely this separation that underpinsthe thermodynamical roots of agency’s time orientation.The general situation is therefore clear: the root oftime orientation in an independent agent is thermo-dynamical irreversibility. This underpins independentagency, hence our own sense of openness of the future.This, in turn, gives us the perspective to read even trivialsymmetric interaction in a time oriented manner.What is missing is to unravel a mechanism showinghow the thermodynamical irreversibility can account forthe time orientation of agency and the openness of thefuture it implies. This is what is done in the next section.
IV. MODELLING THE THERMODYNAMICALIRREVERSIBILITY OF AGENCY
Consider an independent agent: a complex unpre-dictable macroscopic system. Say that in the intervalbetween the times t a and t b it acts on the macroscopicworld causing an effect. Say it can choose between N alternatives in its action. Consider the time evolution ofthe macroscopic state of the world, including the agentitself, and call it Q i ( t ) with i = 1 , ..., N labelling the N possible evolutions (or ‘branches’) of the macro-world.The branches have the same history before the actionand differ after-wise, that is Q i ( t ) = Q j ( t ) , for all i, j and t < t a ,Q i ( t ) = Q j ( t ) , for some i, j and t > t b . (1)This describes what an independent agent, capable ofchoosing, does.The internal dynamics of the agent can be a complexcomputation about possible futures, based on the mem-ory and a value system incorporated in the agent’s mem-ory or structure (more on this below); it can be a randomprocess influenced by the indeterminism of quantum me-chanics (more on this below), or by microscopic statisticalfluctuations; or it can simply be any classical dynamicstoo complex for us to reconstruct. The relative weightof these components in the indeterminacy of the macro-scopic evolution is irrelevant from the point of view ofphysics, because in all cases it simply amounts to disre-garding some physical links in the evolution.Let’s disregard for the moment quantum indetermin-ism. We picture the situation as follows: a macroscopicdeterministic dynamics gives a good approximation tothe dynamics of each Q i ( t ) for any t , but not in the in-terval t a − t b during which agency acts.The key point is that this is not in contradiction withclassical determinism, because there is a large numberof micro-histories q ( t ) compatible with anyone of thebranches of the evolution in (1). Hence there is noth-ing mysterious in the branching itself: it is just a casewhere the causal closure of the (approximate!) macro-scopic dynamics breaks down (see also [13]). In general,physics is non-linear and large effects of small changes arewell known to happen. From this perspective, agency issimply a situation where scale separation does not hold:nothing puzzling here.What is puzzling, on the other hand, is why thebranching is towards the future. As discussed, since themicrophysics is time reversal invariant, the reason for thetime orientation of the branching can only be the time asymmetry of the macrophysics, namely the second prin-ciple. How does this connection work?Since choosing is irreversible it cannot happen withoutentropy increase. Therefore during the interval t a − t b there must be an entropy increase ∆ S >
0. On the otherhand, suppose we observe the macroscopic evolution. Be-fore the time t a we have no information about whichbranch will the system follow. After the time t b we cansee which branch has been realised, hence we have novelinformation. Where does the information come from?The only possible answer is that I is paid for by the in-crease in entropy ∆ S .A model illustrating how this can happen was devel-oped in [17] to account for the relation between memoryand entropy. Let us adapt it here to the present case.Consider two systems: a system A (Agent) at temper-ature T a and a system W (World) at a lower temperature T w < T a . Assume that the two interact only occasionally,say on average once every T seconds, and weakly, namelywith a long thermalization time τ a ≫ T . Furthermore,say that W , in turn, is formed by N subsystems, alsointeracting weakly among themselves, but with a globalthermalization time τ w ≪ T . Remarkably, these meagreingredients are sufficient to model an agent.From the definition of the thermalization time (on av-erage dT a /dt = − T a /τ a ) the average change of tempera-ture δT a during the interval T , hence at each interaction,is given by δT a T a = − T τ a (2)Assuming for simplicity that the heat capacity of W isinfinite and calling C the heat capacity of A , the aver-age exchanged energy in one interaction is Q = − CδT a ,giving Q = CT a T τ a . (3)This is heat, since it comes from the thermal energy of A .Since τ w ≪ T , in a typical configuration the N subsys-tems of W have thermalised and have equal mean energy,say E i = E , where i = 1 , ..., N . We take the N quanti-ties E i to be macroscopic observables. With a frequencydictated by T , the interaction between A and a randomvariable of W happens. Because of the second law, it ismore likely that energy is transferred from A to W thanviceversa. On average, at each interaction an amount Q of energy is transferred to one of the N components of W , say i = ˆ i . After the interaction and for a time of theorder of τ w , the energy of one of the N components of W is higher than the others. Therefore the macroscopicstate of the system around an interaction happening ata time t o is described by E i ( t ) = E, for t < t o , (4) E i ( t ) = E, for i = ˆ i and t > t o , (5) E i ( t ) = E + Q, for i = ˆ i and t > t o , (6)which satisfies (1), and is therefore an example of agency.Thus, the simple thermodynamical ingredients above cangive rise to a system that chooses and influences the fu-ture .The interaction selects one out of N alternative, pro-ducing an amount I = log N (7)of information. The process is irreversible, because heatmoves from a hot to a cold body, and produces an entropyincrease. ∆ S ∼ QT w − QT a ∼ C T τ a ∆ TT w , (8)where ∆ T = T a − T w . A necessary condition for theinformation to be accounted for is I < ∆ S, (9)because information must come from somewhere. Usingthe equations above, this gives N < T τa C ∆ TTw . (10)This equation bounds the possibility of choosing betweenalternatives, at given thermodynamical parameters. Inparticular, it shows that a non-vanishing temperature dif-ference ∆ T is needed to have a choice.To get a sense of this bound, consider it in a very simplecase. Consider a minimal choice between 2 alternatives,namely N = 2; using T ≪ τ a we have C ∆ T ≫ k T w (11)where we have reinserted the Boltzmann constant k = 1for clarity. The left hand side of this equation is theexcess thermal energy in the agent, while the right handside is the average energy per degree of freedom in theworld. That is: in order to be able to choose, the agentsmust have enough energy to stand up above the thermalenergy of the world.Crucially, there is no reduction of entropy in choosing:there is increase in entropy, contrary to what appearsin the picture where the physics of the agent is disre-garded. Choosing is a conventional irreversible process,and it happens because it is statistically favoured, as allirreversible processes do.Before concluding, we comment on two points that weleft open: top-down causation and the role of quantumtheory. A. Top down causation
Defenders of top-down causation point out that it maybe possible to account for the choice of an agent in termsof high-level concepts. For instance, a choice can be mo-tivated by a value system, a calculation about the future, respecting a rule or a moral obligation, knowledge, mem-ory, a computer program, or similar high-level notions.This is obviously true, and does not alter the picturegiven above, for the following reason.High-level concepts make sense autonomously and per-mit us to predict events, but they nevertheless superveneon microphysics. That is, two situations that differ intheir high-level description cannot be identical in theirmicrophysics. For instance: it makes sense to under-stand the behaviour of a computer in terms of its soft-ware rather than thinking in terms of the forces on itselementary particles; but to have different software wenecessarily need a different configuration in the elemen-tary particles. Equivalently: it makes sense to under-stand the behaviour of a person in terms of her moralvalues, but to have different moral values must be ac-companied by something different in the microphysics,perhaps in some synapses in the brain.Now, if high-level concepts are sufficient to accountfor behaviour, this is a normal case of causal closure ofa coarse-grained account of the events. High-level con-cepts, from this perspective, are normal macroscopic vari-ables. We are thus in the case of an internal agent, forwhich it is possible to account for the choice: there isno entropy production in the choice, and the choice isfully determined by the macrophysics. A computer play-ing chess, for instance, choses a move on the basis ofrules. This is an unproblematic case of causal closure ofa macroscopic description.If, on the contrary, high level concepts are not suffi-cient to account for behaviour, then we are back to themicro/macro context. Something else is doing the choice:if it is not the macrophysics, it must be the microphysics.There are always very many micro-histories compatiblewith any given high-level account, leaving space for thebranching.Neither case conflicts with the causal closure of the mi-croscopic physics. Ultimately, agency is always nothingelse than ignoring some physical links. B. Quantum theory
I have framed the discussion in terms of classical me-chanics, because including probabilities complicates thelanguage. But nothing substantial changes in the aboveif quantum mechanics is taken into account.Microscopic time reversal invariance is not broken byquantum randomness [23, 24]. The predictions of quan-tum mechanics are formulated in terms transition proba-bilities. These do not distinguish between past and futureand are time reversal invariant (CPT invariant in quan-tum field theory). The discussion in this paper, on theother hand, clarifies the origin of the time asymmetry inour conventional use of quantum theory. We routinelyinterpret quantum transition probabilities as time ori-ented, namely we routinely read them as probabilitiesfor future events given past events; but this is perspec-tival. It is because we are agents that can influence thefuture, immersed in a time oriented macroscopic world,that we do so. Therefore the time orientation of the com-mon reading of quantum probabilities is just perspectival.As shown, this perspectival time orientation, in turn, isultimately sourced by the arrow of time of the secondprinciple, via our own agency.Quantum theory does not change anything regardingthe distinction between microphysics and macrophysics,either. For the sake of the current discussion quantumindeterminism can be treated as due to unaccounted de-grees of freedom. If one wish to, one can even do so ex-plicitly by using an interpretation of quantum theory likethe de Broglie-Bohm hidden variable one, where indeter-minism is indeed statistical ignorance, or Many Worlds,where indeterminism is indexical, namely ignorance ofthe branch in which we are located. Alternatively, onemay simply remember that in order to affect the macro-world, quantum indeterminism needs decoherence, whichis precisely based on disregarding degrees of freedom.Whether the causal closure of the macroscopic descrip-tion of the world is in principle accounted by some under-lying classical deterministic microphysics or by quantumrandomness is irrelevant for the understanding of agency. V. CONCLUSIONS: MEMORY AND THECREATION OF INFORMATION
We have a strong feeling that we cannot influence thepast, but we can influence the future. This seems to con-flict with the time (CPT) reversal invariance of funda-mental physics. But is not. We have this feeling becausetruly we can affect the macroscopic future but not themacroscopic past. The macroscopic world we work withhas a fixed past determined by abundant present tracesand memories [17], while it is compatible with a numberof different futures, that do depend on what happens inour brain. This is the openness of the future that ourfeeling veridically captures.This openness of the future leaves ample space for sub-tle high level processes to influence the macroscopic fu-ture. Our sense of being free to decide is clearly rootedhere. It is in this sense, that, as Ismael puts it: ‘PhysicsMakes Us Free’ [20].The microscopic account is a wholly different story, butis of little relevance for our experience and feelings, since,by definition, we do not access it.Independent agency is a description of the macroscopic dynamics of an interaction between an agent and theworld which: (i) is unpredictable, (ii) is irreversible,(iii) produces a (macroscopically) detectable effect on theworld in the future, and (iv) produces information. Thereare remarkable similarities between this and the modelfor traces, or ‘memories’, described in [17].Both memory and agency are events that leave a tracein the macroscopic domain. The difference is that theroles are in a certain sense exchanged: in the case of agency, it is the agent that leaves a trace on the exter-nal macroscopic world; while memory is a trace left bythe world on the memory system. Both phenomena needlong thermalization times, namely quasi-stable system,to hold the memory or the effect of the action. Both needa disequilibrium in the past, to account for orientationand irreversibility. Both can be understood as macro-scopic phenomena pertaining to a coarse grained pictureof the world, and make no sense at the microscopic level(except in metaphorical ‘anthropocentric’ language).Agency is time oriented because it is a macroscopicphenomenon driven by an entropy gradient (hence ulti-mately by the past hypothesis). The model presented inSection IV shows that system separation, past tempera-ture difference, and long thermalization times are meagreelements nevertheless sufficient to model this thermody-namical roots of agency. In turn, our time orientation asagents compels us to look at mechanical interactions ina time oriented manner [15].The most interesting aspects of the two phenomena isthat they both produce information. In agency, infor-mation can be recognised, in Shannon’s sense, as the in-stantiation of one among a number of possibilities. In thecase of memory, information is what Shannon calls ‘rel-ative information’: physical correlation between a pastmacroscopic event and its trace.In both cases, the information is generated by increas-ing entropy. Eq (10) gives the maximal information thatcan be produced in choosing, at given thermodynamicalparameters. It analogous to bound on the informationproduced by the formation of memory derived in [17].Low entropy is a form of information because a lowerentropy state amounts to a more selective informationabout the microphysics (a zero entropy macrostate isa state that has maximal information about the mi-crophysics: the microstate is unique). Memory andagency utilise the information stored in low entropy andtranslate it into information readable in the macroscopicworld. In fact, they both can be viewed as mechanismsthat generate macroscopic information.Macroscopic information, stored in human memory, inDNA molecules, in computer messages, in books, in nar-ratives, in software codes, in records of any form, musthave been ultimately produced by physical mechanisms.Traces of the past and decisions by agents —possibly inturn themselves affected by memories of the past— aremajor sources of everything we call information. In bothcases, information is created, in a statistically favouredmanner, at the expenses of low entropy, in accordancewith the second principle. In a fully thermalised situa-tion, there is no space for memories or for agents.The entire informational universe formed by thebiosphere and by culture can therefore perhaps beviewed, from this perspective, as formed by informationproduced by a mechanism of the form described here.***I am deeply indebted with Jenann Ismael: severalideas of this paper developed in conversations with her.Thanks to David Albert for a very insightful criticisms toan early draft of this paper, crucial for me. This work wasmade possible through the support of the FQXi Grant FQXi-RFP-1818 and of the ID
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