Journal of Cosmology, 2011, Vol. 14.
JournalofCosmology.com, 2011
The Dissipative Brain and
Non-Equilibrium
Thermodynamics
Walter J. Freeman, Ph.D.1, and
Giuseppe Vitiello, Ph.D.2, Department of Molecular & Cell Biology, Division of
Neurobiology, University of California at Berkeley,
Berkeley CA. 1
Facoltà di Scienze Matematiche, Fisiche e Naturali e
Istituto Nazionale di Fisica Nucleare Università di
Salerno, Italia
2
Abstract
Cognitive neurodynamics describes the process by which
brains direct the body into the world and learn by
assimilation from the sensory consequences of the brain
directed actions. Repetition of the process comprises the
action-perception cycle by which knowledge is
accumulated in small increments. The global memory
store is based in a rich hierarchy of attractor
landscapes comprising a library of increasingly
abstract generalizations. In this paper we briefly
summarize the dissipative many-body model of brain
which provides the theoretical scheme aimed to describe
the basic dynamics underlying the neurological activity
described above.
Energy dissipation as heat manifests itself in the
disappearance and emergence of the ground state
coherence. The emergence of classicality out of the
microscopic dynamics is a central feature of the
dissipative many-body model.
KEY WORDS: Brain modeling, Many-body physics,
Coherence, Quantum Dissipation, Consciousness,
Observations and data analysis carried on in the past
decades (Freeman, 1975-2006) have shown that the
brains of animal and human subjects engaged with their
environments exhibit coordinated oscillations of
populations of neurons, changing rapidly with the
evolution of the relationships between the subject and its
environment, established and maintained by the actionperception cycle (Freeman, 2004a-2006; Vitiello, 2001;
Freeman & Vitiello, 2006-2010).
Our analysis of electroencephalographic (EEG) and
electrocorticographic (ECoG) activity has shown that
cortical activity during each perceptual action creates
multiple spatial patterns in sequences that resemble
cinematographic frames on multiple screens (Freeman,
Burke and Holmes, 2003; Freeman, 2004a,b). In this
paper we will briefly review some of the features of the
dissipative model of brain which has been formulated in
recent years (Vitiello, 1995, 2001; 2004; Freeman &
Vitiello, 2006- 2010).
The sources of these patterns are identified with large
areas of the neocortical neuropil (the dense felt-work of
axons, dendrites, cell bodies, glia and capillaries forming
a continuous sheet 1 to 3 mm in thickness over the entire
extent of each cerebral hemisphere in mammals). The
carrier waves of these patterns are identified with narrow
band oscillations (±3-5 Hz) in the beta (12-30 Hz) and
gamma (30-80 Hz) ranges (Freeman, 2005, 2006, 2009).
The change in the dynamical state of the brain with each
new frame resembles a collective neuronal process of
phase transition (Freeman & Vitiello, 2006-2009)
requiring rapid, long-distance communication among
neurons for almost instantaneous re-synchronization of
vast numbers of neurons (106 to 108).
Several mechanisms such as dendritic loop currents,
propagated action potential, and diffusion of chemical
transmitters have been proposed to explain the observed
temporal precision and fineness of spatial texture of
synchronized cortical activity. The documented rapid
changes in synchronization over distances of mm to cm
(Freeman, 2005) are incompatible with the mechanisms
of long-range diffusion and the extracellular dendritic
currents of the ECoG, which are much too weak. The
length of most axons in cortex is a small fraction of the
observed distances of long-range correlation, which
cannot easily be explained even by the presence of
relatively few very long axons creating small world
effects (Barabásí, 2002).
The occurrence of such collective neuronal processes
with their observed properties has suggested to us to use
the formalism of many-body field theory to model the
brain functional activity. In such an approach the brain
appears to be a macroscopic quantum system
(Umezawa, 1993; Vitiello, 1995, 2001, 2004; Freeman &
Vitiello, 2006-2010), namely a system whose
macroscopic behaviour cannot be explained without
recourse to the microscopic dynamics of its elementary
components. Here it has to be specified that neurons, glia
cells and other microscopic organelles are considered to
be classical elements in the dissipative many-body
model.
The quantum degrees of freedom are the quanta of the
electrical dipole fields of the biomolecules and water
molecules, the matrix in which all the biological cells are
embedded. The existence of macroscopic quantum
systems in other physical domains, such as crystals,
ferromagnets, superconductors, etc., shows indeed that
the domain of validity of quantum field theory (QFT) is
not restricted to the microscopic physics (Umezawa,
1993; Blasone, Jizba and Vitiello, 2011).
The use of the QFT formalism in the study of the brain
does not mean that the traditional classical tools of
biochemistry and neurophysiology might be abandoned.
Rather, these classical tools might receive further boost
from the understanding of the underlying microscopic
dynamics.
It was in such a line of thoughts that Ricciardi and
Umezawa (Ricciardi & Umezawa, 1967; Stuart,
Takahashi and Umezawa, 1978; 1979) formulated the
many-body model of brain.
In the ‘40s, motivated by his experimental observations,
Karl Lashley wrote: "Here is the dilemma. Nerve
impulses are transmitted from cell to cell through definite
intercellular connections. Yet all behaviour seems to be
determined by masses of excitation. ... What sort of
nervous organization might be capable of responding to a
pattern of excitation without limited specialized paths of
conduction? The problem is almost universal in the
activities of the nervous system" (Lashley, 1942, p. 306).
The observations by Lashley were confirmed by other
neuroscientists, such as Karl Pribram who proposed
(Pribram, 1971) a holographic model to explain
psychological field data. The understanding of such data
in the frame of the available theory of condensed matter
systems was the aim of the many-body model. The
crucial mechanism on which the model is based is the
one of the spontaneous breakdown of symmetry (SBS).
QFT is based on a dual level of description: the
dynamical level, where the dynamical field equations and
their symmetry properties are postulated, and the
physical level of the fields in terms of which the
observables are described. The whole QFT
computational machinery consists in solving the
dynamical field equations (the dynamical level) in terms
of physical fields acting on the space of the physical
states (the physical level). The point is that there are
many "non-equivalent copies" of spaces of physical
states. In other words, there are (infinitely) many
possibilities in which the same basic dynamics may be
realized in terms of physical observables: there are many
possible "physically different worlds" in which the same
basic dynamics may manifest itself. "Different" (or, in
mathematical language, "non-unitarily equivalent")
spaces of physical states means that the physical
observables acquire different values depending on which
one is the space of physical states (the world) we choose
(or we are forced by some specific boundary conditions)
to work with. Due to such a peculiar property of QFT (it
is this property that makes QFT fundamentally different
from Quantum Mechanics!!), it may happen that the
symmetry properties of the space of the physical states
are not the same as the ones of the basic dynamical
equations: the basic symmetry gets broken in the process
of mapping the dynamical level to the physical level of
description.
Since, we have access to (we "live" in) this last level, it is
the dynamically rearranged symmetry the one that we
observe, not the one of the basic dynamical field
equations. In particular, in the process of symmetry
breakdown an observable variable emerges, called the
order parameter, which characterizes the macroscopic
behaviour of the physical system, as a whole. The order
parameter expresses in a highly non-linear way the
microscopic behaviour of the myriads of elementary
constituents of the system. The order parameter thus
emerges as a classical field and marks the transition from
the microscopic scale to the macroscopic scale. It is a
measure of the complexity of the basic dynamics ruling
the system, which cannot be reduced to or derived from
the sum of the behaviours of the elementary components
(Umezawa, 1993; Blasone, Jizba and Vitiello, 2011).
In our model we conceive the order parameter as the
density of the synaptic interactions at every point in the
cortical neuropil, and we interpret the ECoG recorded at
each point as an experimentally observable correlate of
the neural order parameter.
One further point, turning out to be a very important one
in our brain modelling, is that the symmetry breakdown
is spontaneous: this means that, under given boundary
conditions (e.g. at given temperature), the specific form
into which symmetry gets rearranged is chosen by the
dynamics of the system, i.e., by its inner dynamical
evolution. SBS is thus a dynamical process, different
from the explicit breakdown obtained by introducing at
the dynamical level constraints explicitly violating the
symmetries of the basic field equations.
In neurobiological terms, these constraints are stimuli,
typically an impulse in the form of a click, flash, or
electric shock, able to reduce the functional activity of
the brain into slavery. In the SBS, instead, the external
stimulus acts only as a trigger of the inner evolution.
One central theorem in QFT states that SBS implies the
existence of particles, called Nambu- Goldstone (NG)
modes or fields, that are massless and are bosons, i.e.,
they can be collected or condensed in the same physical
state without any restriction on their number and, since
they are massless, they can span the whole system
volume and are therefore responsible for the occurrence
of long-range correlations, namely of the ordering which
thus is established in the system: Order appears as a
result of the symmetry breakdown; order is lack of
symmetry. The lowest energy state, called the vacuum
or the ground state, thus appears as a condensate of such
NG (Nambu- Goldstone) modes.
The order parameter provides a measure of the
condensation density of the NG modes in the vacuum
state and therefore a measure of the long-range
correlation. On the other hand, the condensation process
is described by the transformation B -> B + α, where B
denotes the NG field and α is complex number, α = |α|
exp(iθ), which may also depend on space-time. In such a
last case, we have space-time dependent condensation;
otherwise we have homogeneous condensation. It is well
known that the transformation B -> B + α generates a
coherent state. The number of the condensed NG field
indeed is given by |α|² and thus we see that the vacuum is
characterized by an unique phase θ: the NG modes share
the same phase, which is characteristic of coherent states.
In the Ricciardi and Umezawa (RU) brain model,
memory is described by SBS triggered by an external
stimulus; long-range correlations are then generated by
the inner dynamics of the brain and NG modes are
condensed in the vacuum; the memory code is taken to
be the condensation density |α|². Note that the memory
thus associated to a specific triggering stimulus is not a
representation of that stimulus (Freeman & Vitiello,
2006-2010).
Fhrölich (1968) and Del Giudice et al (1985; 1986) have
proposed that the electrical polarization density arising
from the water matrix and the other biomolecules might
be considered to be the order parameter in the study of
biological matter, also with reference to the formation
and the dynamical properties of microtubules in the cell,
thus characterizing the living phase of the matter.
Jibu and Yasue (1995) and Jibu, Yasue and Pribram
(1996) then proposed that the symmetry breakdown in
the RU [Ricciardi and Umezawa brain model, memory is
described by SBS triggered by an external stimulus;
long-range correlations are then generated by the inner
dynamics of the brain and NG modes are condensed in
the vacuum] model was the one of the rotational
symmetry of the electrical dipoles. We propose a further
refinement: the order parameter accounts for the density
of dipole moment exerted by neuron populations at each
point in the neuropil through synaptic interactions.
Moreover, the model has been extended to include the
dissipative dynamics describing the fact that the brain is
permanently open on the external world (Vitiello, 1995;
2001). The starting observation on which the
dissipative model is based is indeed that there is no
question that brains are open thermodynamic
systems operating far from equilibrium. Brains burn
glucose to store energy in glycogen ("animal starch") and
high-energy adenosinetriphosphate (ATP), and in
transmembrane ionic gradients; they dissipate free
energy in proportion to the square of the ionic current
densities that are manifested in epiphenomenal electric
and magnetic fields, and that mediate the actionperception cycle (Freeman & Vitiello, 2006). Brain
imaging techniques such as fMRI are indirect measures
of metabolic dissipation of free energy, relying on
secondary increases in blood flow and oxygen depletion.
The dendrites dissipate 95% of the metabolic energy in
summed excitatory and inhibitory ionic currents, the
axons only 5% in action potentials that carry the summed
output of dendrites by analog pulse frequency
modulation. One of the main tasks of the dissipative
model is thus the one of formulating the thermodynamic
features involved in the action-perception cycle. The
model indeed shows how the process of energy
dissipation as heat manifests itself in the disappearance
and emergence of coherence.
On the other hand, dissipation enables brains to form an
indefinite variety of different ground states, which is
prerequisite for high memory capacity (Vitiello, 1995:
2001). Indeed, introducing dissipation solves the memory
capacity problem plaguing the RU model [Ricciardi and
Umezawa brain model, memory is described by SBS
triggered by an external stimulus; long-range correlations
are then generated by the inner dynamics of the brain and
NG modes are condensed in the vacuum], where any
subsequent stimulus would trigger a new NG
condensation erasing the previous condensate (memory
overprinting). In the dissipative model, under the
influence of an external stimulus, the brain inner
dynamics selects one of the possible (inequivalent)
ground states, each of them thus being associated to a
different memory. Infinitely many memories may thus be
stored and, due to the unitarily inequivalence of the
(vacuum) states, they are protected from reciprocal
interference. In the dissipative model we regard the NG
condensate as an expression of a transiently retrieved
memory (thought, percept, recollection) that has been
accessed by a phase transition.
The possibility to exploit the whole variety of unitarily
inequivalent vacua arises as a consequence of the
mathematical necessity in quantum dissipation to
"double" the system degrees of freedom so as to include
the environment in which the brain is embedded. That
reflective fraction of the environment is thus described as
the Double of the system, which turns out to be the
system time- reversed copy. The entanglement between
the brain and its environment is thus described as a
permanent coupling, or dynamic dialog between the two,
which may be related to consciousness mechanisms.
Consciousness thus appears as a highly dynamic process
rooted in the dissipative character of the brain dynamics,
which, ultimately, is grounded into the non-equilibrium
thermodynamics of its metabolic activity.
In recent years, the dissipative model has been developed
also considering the available experimental observations
and data analysis (Freeman & Vitiello, 2006-2010). The
reader can find in the quoted literature a list of properties
and predictions of the model, as compared to
observations, which here for brevity we do not report.
The data analysis shows that one can depict the brain
non-linear dynamics in terms of attractor landscapes.
Each attractor is based in a nerve cell assembly of
cortical neurons that have been pair-wise co-activated in
prior Hebbian association and sculpted by habituation
and normalization (Kozma & Freeman, 2001). Its basin
of attraction is determined by the total subset of receptors
that has been accessed during learning. Convergence in
the basin to the attractor gives the process of abstraction
and generalization to the category of the stimulus.
The memory store is based in a rich hierarchy of
landscapes of increasingly abstract generalizations
(Freeman, 2005; 2006). The continually expanding
knowledge base is expressed in attractor landscapes in
each of the cortices.
In conclusion, the dissipative many-body model of brain
provides the theoretical scheme aimed to describe the
basic dynamics underlying the neurological activity. It
illustrates the observed formation and properties of
imploding and exploding conical phase gradients and the
occurrence of null spikes that have been identified in
multichannel records of ECoG signals. Energy
dissipation is shown to incorporate the observed feature
of null spikes, which are transient extreme reduction in
macroscopic energy, in which order disappears and
symmetry is momentarily re-established.
The extreme localization in space, time and spectrum
(Freeman, 2009) indicate that the null spikes are
observable manifestations of a singularity by which the
symmetry is broken. Classical Maxwell equations
and current fields are derived from the
quantum dynamics (Freeman & Vitiello,
2010), thus confirming that functional aspects
of brain dynamics are derived as macroscopic
manifestations of the underlying many-body
dynamics: the emergence of classicality out of
the microscopic dynamics thus appears to be a
central feature of the dissipative many-body
model. The model also describes the size, number and
time dependence of the transient non-homogeneous
patterns of percepts appearing during non-instantaneous
phase transitions, such as those observed in brain.
Further developments of the dissipative model
considering other features of non-equilibrium neuronal
thermodynamics are under study.
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