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 action-perception 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 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|˛ 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|^˛. 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 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 action- perception 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, 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.