I always thought that thermodynamics/statistical physics is effective theory – statistical result of some fundamental physics below, but recently there became popular theories starting from ‘entropic force’ as fundamental (basing on holographic scenarios, like in http://arxiv.org/abs/1001.0785 ).

For a simple mathematician like me it sounds like a nonsense – in fundamental theory describing evolution of everything there should be one concrete history of our Universe – there is no place for direct probabilities of scenarios required to define e.g. entropy.

I was taught that to introduce effective local thermodynamical parameters to given concrete situation, for each point we average inside some ball around it to get for example local entropy or temperature, what allows to work on simplified statistically typical behavior.

So I wanted to ask if someone could explain why we can even think about fundamental ‘entropic’ theories?

To start the discussion I would like to briefly remind/discuss looking clear for me distinction between deterministic and stochastic/thermodynamical models:

DETERMINISTIC models – the future is completely determined

- evolution of gas in a tank is full dynamics of all its particles - for given valve opening there escaped concrete number of particles,

- it's usually Lagrangian mechanics of some field – there is some scalar/vector/tensor/’behavior of functional'(QFT) in each point of our spacetime, such that ‘the action is optimized’ – each point is in equilibrum with its four-dimensional neighborhood (spacetime is kind of ‘4D jello’),

- evolution equations (Euler-Lagrange) are HYPERBOLIC PDE - linearized behavior of coordinates in the eigenbase of the differential operator is

d_tt x = - lambda x

(0 < lambda = omega^2 )

so in linear approximation we have superposition of rotation of coordinates – ‘unitary’ evolution – and so such PDE are called wavelike – the basic excitations on water surface, in EM, GR, Klein-Gordon are just waves,

- the model has FULL INFORMATION – there is no place for direct probability/entropy in electromagnetism, general relativity, K-G etc. – the model has some TIME (CPT) SYMMETRY INVARIANCE (no 2nd law of thermodynamics – there is still unitary evolution in thermalized gas or a black hole)

THERMODYNAMICAL/STOCHASTIC models – there is some probability distribution among possible futures

- gas in a tank is usually seen as thermalized, what allows to describe it by a few statistical parameters like entropy (like sum of –p*lg(p) ) or temperature (average energy per degree of freedom) - for a specific valve opening, the number of escaped particles is given by a probability distribution among possible scenarios only,

- it is used when we don’t have full information or want to simplify the picture – so we assume some mathematically universal STATISTICAL ENSEMBLE among POSSIBLE SCENARIOS (like particle arrangements http://en.wikipedia.org/wiki/Microcanonical_ensemble ) – optimizing entropy (uniform distribution) or free energy (Boltzmann distribution),

- thermodynamical/stochastic evolution is usually described by discussion-like: PARABOLIC PDE – linearized behavior of coordinates in the eigenbase of the

differential operator is

d_t x = - tau x

(tau - ‘mean lifetime’ )

so in linear approximation we have exponential decay (forgetting) of coordinates – evolution is called thermalization: in the limit there survive only ones with the smallest tau – we call it thermodynamical equilibrium and usually can be describe using just a few parameters,

- these models don’t have time symmetry – we cannot fully trace the (unitary?) behavior so we have INFORMATION LOST – entropy growth – 2nd law of thermodynamics.

Where I’m wrong in this distinction?

I agree that ‘entropic force’ is extremely powerful, but still statistical result – for example if while random walk instead of maximizing entropy locally what leads to Brownian motion, we do it right: globally, we thermodynamically get going to the lowest quantum state probability density – single defects create macroscopic entropic barriers/wells/interactions:

http://demonstrations.wolfram.com/Ge...opyRandomWalk/

For me the problem with understanding quantum mechanics is that it’s between these pictures – we usually have unitary evolution, but sometimes entropy grows while wavefunction collapses – there is no mystical interpretation needed to understand it: entropy maximizing from mathematically universal uncertainty principle is just enough ( http://arxiv.org/abs/0910.2724 )

What do you think about this distinction?

Can thermodynamical models be not only effective (result), but fundamental (reason)?

Can quantum mechanics alone be fundamental?