If we, for simplicity's sake, take "particles" to mean, macromolecules, then yes, they do. The quantum version is slightly trickier, but it does produce a "unique" outcome, it's just slightly wibbly.
Let's ignore quantam mechanics for the moment. In what sense is physics (as it is currently understood) explain the molecular organization of neural activity?
Rather than just repeat myself, I'll try to give a concise but thorough enough account of the research behind my assertion that even without getting into quantam mechanics physical laws do not uniquely determine states of the brain.
From Davies' paper in
Re-Emergence of Emergence (Oxford University Press, 2006):
"Recent work by Max Bennett (Bennett and Barden, 2001) in Australia has determined that neurons continually put out little tendrils that can link up with others and effectively rewire the brain on a time scale of twenty minutes! This seems to serve the function of adapting the neuro-circuitry to operate more effectively in the light of various mental experiences (e.g. learning to play a video game). To the physicist this looks deeply puzzling. How can a higher-level phenomenon like ‘experience’, which is also a global concept, have causal control over microscopic regions at the sub-neuronal level? The tendrils will be pushed and pulled by local forces (presumably good old electromagnetic ones). So how does a force at a point in space (the end of a tendril) ‘know about’, say, the thrill of a game?"
Another huge factor is the massive dynamical synchonization of neural activity. An introductory book on a dynamical systems approach to neural activity may be found here:
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. It does not assume a familiarity with dynamical systems or too much in the way of neuroscience, but a knowledge of multivariate calculus, basic chemistry, and some basic familiarity with neurophysiology is essential. The last chapter is devoted to synchonization, which is also the subject of the book
Emergence of dynamical order: synchronization phenomena in complex systems. The final chapter examines neural networks in particular:
"..synchronization links together processes in distant parts of the brain. According to a popular hypothesis, development of transient synchronous clusters in neural networks spanning the whole brain is responsible for the appearence of distinct mental states which make up the flow of human consciousness.
When large-scale synchronization of neuronal processes is discussed, one should avoid the mistake of assuming that it merely results from the synchonization of states of individual neurons. If this were the case, the whole brain or large parts would have behaved just like a single neuron....We show that interaction between networks can lead to mutual synchronization of their activity patterns and to spontaneous seperation of the enseble into coherent network clusters."
It is this complexity which allows a
non-reductionist account of neural activity. From Scott's paper in
Evolution and Emergence (Oxford University Press, 2007):
"Under [strong downward causation], it is supposed that upper-level phenomena can act as efficient causal agents in the dynamics of lower levels. In other words,
upper-level organisms can modify the physical and chemical laws governing their molecular constituents."
The complexity of neurons is due to their networking capacity which allows emergent and irreducible structures: "In network-level models, identical neurons are interconnected to exhibit emergent system functions...In the framework of neural complex systems,
the microscopic level of interacting neurons is distinguished from the macroscopic level of global patterns produced as cell assemblies by self-organization...Large and complex real-world systems, which include neurons and neural populations, are noisy, nearly infinite-dimensional, non-stationary and non-autonomous...The discovery that brain dynamics operates in chaotic domains has profound implications for the study of higher brain function. A chaotic system has the capacity to create novel and unexpeted patterns of activity."
-from Klaus
Symmetry and Complexity (World Scientific Publishing Co., 2005).
This is not to say that all or even most neuroscients agree that the complexity of neural activity make it ontologically indeterminant rather than epistemically indeterminant, but "baseline state indeterminacy [of the brain] can br ontological, that is, the very structure of the brain dictates indeterministic states, independently of any observation..." -from Gur, Contreraras, and, Gur's paper in
Indeterminacy: The Mapped, the Navigable, and the Uncharted (MIT press, 2009).
Self-organisation is
caused by the reductionist physical laws governing each unit. It must be, otherwise they wouldn't be very good laws, would they?
Well they wouldn't be laws we fully understand. But then, that's nothing new. However, research into dynamical systems especially that of the brain reveals a great deal of evidence against 1) the type of causation argued in this thread and 2) reductionist physics:
"The attractor determines the response, not the particular stimulus. Unlike the view proposed by stimulus-response reflex determinism, the dynamics
give no linear chain of cause and effect from stimulus to response that can lead to the necessity of environmental determinism." from Freeman's paper in
Does Consciousness Cause Behavior? (MIT press, 2006). He concludes by noting the inability of neurscientists to account for the global activity of neural networks by way of locality or reductionist physical laws.